<rss xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" version="2.0">
  <channel>
    <title>MaplePrimes - Maple 2019 Posts and Questions</title>
    <link>http://www.mapleprimes.com/products/Maple/Maple 2019</link>
    <language>en-us</language>
    <copyright>2026 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
    <generator>Maplesoft Document System</generator>
    <lastBuildDate>Thu, 09 Apr 2026 20:50:15 GMT</lastBuildDate>
    <pubDate>Thu, 09 Apr 2026 20:50:15 GMT</pubDate>
    <itunes:subtitle />
    <itunes:summary />
    <description>Maple 2019 Questions and Posts on MaplePrimes</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - Maple 2019 Posts and Questions</title>
      <link>http://www.mapleprimes.com/products/Maple/Maple 2019</link>
    </image>
    <item>
      <title>How to mark intersection points</title>
      <link>http://www.mapleprimes.com/questions/242188-How-To-Mark-Intersection-Points?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;Suppose I am plotting a 2D plot and want to highlight the point where two lines intersect. I would like to display this intersection point inside the plot in black font, mark it with an arrow or some visual highlight, and clearly label it. How can I do this?&lt;/p&gt;

&lt;p&gt;Additionally, instead of using different colours (blue, green, red) for the lines, I want to distinguish them using different line styles such as solid, dotted, and long-dashed lines. How can I make these changes?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="A6D4859DD033E1604765AE9C9A8570C4"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=315428_Answer/d400794a0b3514e085c6de2763d38a2c.gif" style="vertical-align:-7px" width="81"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)" height="23" src="/view.aspx?sf=315428_Answer/f5ff44f996c4c8bb5fde50200c18a3fa.gif" style="vertical-align:-7px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=315428_Answer/e60a7913807ffdd495d94f0c0b6d56de.gif" style="vertical-align:-7px" width="90"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=315428_Answer/6a3fdc7ca9f953e7992a3f430947bea1.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_w := b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*((Cr*b-1)*d+b))*(delta+Cn-Pr-1))^2*d/(8*(Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))" height="151" src="/view.aspx?sf=315428_Answer/89a87c020378673118735e498ddc1ec7.gif" style="vertical-align:-135px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(1/8)*b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*(Cr*b-1)*d+2*b)*(delta+Cn-Pr-1))^2*d/((Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))" height="75" src="/view.aspx?sf=315428_Answer/afceacc9a8c8836f1d5325763607569b.gif" style="vertical-align:-55px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&amp;nbsp;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&amp;nbsp;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_D := (Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*(Cr*b-1))*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*(((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+rho0^2*b*alpha))*((Cr*b-1)*d+b)^2)" height="157" src="/view.aspx?sf=315428_Answer/f951eec41adf99e377c22e65182ae73e.gif" style="vertical-align:-131px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*Cr*b-2)*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+8*rho0^2*b*alpha)*((Cr*b-1)*d+b)^2)" height="101" src="/view.aspx?sf=315428_Answer/c46e9abcbf8d7909c38e17d3eff3fbb9.gif" style="vertical-align:-83px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_S := ((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+3*t)*alpha*b+((g*i2-a)*Cr+2*Pr-2*Crm-2*c+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(2*(-sigma*t-Cn+Pr-delta+1))*((Cr*b-1)*d+b))^2*b*d/((8*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))*(Cr*b*d+b-d)^2)" height="134" src="/view.aspx?sf=315428_Answer/58d52171957fbd674eaec5f515709c80.gif" style="vertical-align:-118px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+3*t)*alpha*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(-2*sigma*t-2*Cn+2*Pr-2*delta+2)*((Cr*b-1)*d+b))^2*b*d/((8*((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-16*b*d*(delta-1))*(Cr*b*d+b-d)^2)" height="104" src="/view.aspx?sf=315428_Answer/5fff90f5642ea12a0f42478a63b263dd.gif" style="vertical-align:-83px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&amp;nbsp;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=315428_Answer/31a0d3017558ddcef61a6de39eadfcbe.gif" style="vertical-align:-6px" width="6"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="DATA1 := [delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]" height="46" src="/view.aspx?sf=315428_Answer/ab13d1e32c99cb55f67e65d0dea85514.gif" style="vertical-align:-27px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="[delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]" height="46" src="/view.aspx?sf=315428_Answer/f52424d218f38eda7c4e6f6f6259aa0b.gif" style="vertical-align:-27px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="P11 := subs(DATA1, M_w); P21 := subs(DATA1, M_D); P31 := subs(DATA1, M_S)" height="23" src="/view.aspx?sf=315428_Answer/df5a491b7931054a1216ffd6aa369b9d.gif" style="vertical-align:-6px" width="547"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="0.9301486586e-2" height="23" src="/view.aspx?sf=315428_Answer/e416289e6ae337f4018ea16ab3757e8c.gif" style="vertical-align:-6px" width="157"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="4.251178959*(-0.4764573140e-1+0.4030e-2*sigma)^2" height="30" src="/view.aspx?sf=315428_Answer/6278071ec2473b5fd609c12cb1768387.gif" style="vertical-align:-7px" width="350"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="4.251178959*(-0.4917713136e-1+0.4030e-2*sigma)^2" height="30" src="/view.aspx?sf=315428_Answer/17337cc759bf64a62cd3e8dc1e954f36.gif" style="vertical-align:-7px" width="350"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=315428_Answer/cdca36b55e2842521b4a6abb20bb12be.gif" style="vertical-align:-7px" width="6"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="A1 := plot([P11, P21, P31], sigma = 0 .. .7, color = [&amp;quot;Red&amp;quot;, &amp;quot;Blue&amp;quot;, &amp;quot;Green&amp;quot;], labels = [sigma, `&amp;amp;pi;__m`], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;W&amp;quot;));`, `#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;D&amp;quot;));`, `#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;DS&amp;quot;));`], axis[2] = [color = &amp;quot;#600000&amp;quot;])" height="135" src="/view.aspx?sf=315428_Answer/fd9e3de19840f0d9d3ee2801009a2ed0.gif" style="vertical-align:-116px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="500" src="/view.aspx?sf=315428_Answer/e7684fcbdf20391409c835dd65542f2b.gif" style="border:none" width="500"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="display(A1, pointplot([[X, Y]], symbol = circle, symbolsize = 25, color = blue))" height="96" src="/view.aspx?sf=315428_Answer/b0f95216e278c10fb9a9e038cd5cc5c2.gif" style="vertical-align:-79px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;a href="http://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20(in%20plots%3A-pointplot)%20points%20cannot%20be%20converted%20to%20floating-point%20values"&gt;&lt;span style="color:#ff00ff;font-size: 100%;font-family: Courier New,monospace;font-weight:normal;font-style:normal;"&gt;&lt;u&gt;Error, (in plots:-pointplot) points cannot be converted to floating-point values&lt;/u&gt;&lt;/span&gt;&lt;/a&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=315428_Answer/d8e67d3762be39da27cdbdb65b664249.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=315428_Answer/Manf_profit__t_graph_changes_needed.mw"&gt;Download Manf_profit__t_graph_changes_needed.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Suppose I am plotting a 2D plot and want to highlight the point where two lines intersect. I would like to display this intersection point inside the plot in black font, mark it with an arrow or some visual highlight, and clearly label it. How can I do this?&lt;/p&gt;

&lt;p data-end="595" data-is-last-node="" data-start="382"&gt;Additionally, instead of using different colours (blue, green, red) for the lines, I want to distinguish them using different line styles such as solid, dotted, and long-dashed lines. How can I make these changes?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="A6D4859DD033E1604765AE9C9A8570C4"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=315428_Answer/d400794a0b3514e085c6de2763d38a2c.gif" style="vertical-align:-7px" width="81"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)" height="23" src="/view.aspx?sf=315428_Answer/f5ff44f996c4c8bb5fde50200c18a3fa.gif" style="vertical-align:-7px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=315428_Answer/e60a7913807ffdd495d94f0c0b6d56de.gif" style="vertical-align:-7px" width="90"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=315428_Answer/6a3fdc7ca9f953e7992a3f430947bea1.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_w := b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*((Cr*b-1)*d+b))*(delta+Cn-Pr-1))^2*d/(8*(Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))" height="151" src="/view.aspx?sf=315428_Answer/89a87c020378673118735e498ddc1ec7.gif" style="vertical-align:-135px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(1/8)*b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*(Cr*b-1)*d+2*b)*(delta+Cn-Pr-1))^2*d/((Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))" height="75" src="/view.aspx?sf=315428_Answer/afceacc9a8c8836f1d5325763607569b.gif" style="vertical-align:-55px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&amp;nbsp;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&amp;nbsp;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_D := (Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*(Cr*b-1))*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*(((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+rho0^2*b*alpha))*((Cr*b-1)*d+b)^2)" height="157" src="/view.aspx?sf=315428_Answer/f951eec41adf99e377c22e65182ae73e.gif" style="vertical-align:-131px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*Cr*b-2)*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+8*rho0^2*b*alpha)*((Cr*b-1)*d+b)^2)" height="101" src="/view.aspx?sf=315428_Answer/c46e9abcbf8d7909c38e17d3eff3fbb9.gif" style="vertical-align:-83px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M_S := ((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+3*t)*alpha*b+((g*i2-a)*Cr+2*Pr-2*Crm-2*c+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(2*(-sigma*t-Cn+Pr-delta+1))*((Cr*b-1)*d+b))^2*b*d/((8*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))*(Cr*b*d+b-d)^2)" height="134" src="/view.aspx?sf=315428_Answer/58d52171957fbd674eaec5f515709c80.gif" style="vertical-align:-118px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+3*t)*alpha*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(-2*sigma*t-2*Cn+2*Pr-2*delta+2)*((Cr*b-1)*d+b))^2*b*d/((8*((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-16*b*d*(delta-1))*(Cr*b*d+b-d)^2)" height="104" src="/view.aspx?sf=315428_Answer/5fff90f5642ea12a0f42478a63b263dd.gif" style="vertical-align:-83px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&amp;nbsp;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=315428_Answer/31a0d3017558ddcef61a6de39eadfcbe.gif" style="vertical-align:-6px" width="6"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="DATA1 := [delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]" height="46" src="/view.aspx?sf=315428_Answer/ab13d1e32c99cb55f67e65d0dea85514.gif" style="vertical-align:-27px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="[delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]" height="46" src="/view.aspx?sf=315428_Answer/f52424d218f38eda7c4e6f6f6259aa0b.gif" style="vertical-align:-27px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="P11 := subs(DATA1, M_w); P21 := subs(DATA1, M_D); P31 := subs(DATA1, M_S)" height="23" src="/view.aspx?sf=315428_Answer/df5a491b7931054a1216ffd6aa369b9d.gif" style="vertical-align:-6px" width="547"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="0.9301486586e-2" height="23" src="/view.aspx?sf=315428_Answer/e416289e6ae337f4018ea16ab3757e8c.gif" style="vertical-align:-6px" width="157"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="4.251178959*(-0.4764573140e-1+0.4030e-2*sigma)^2" height="30" src="/view.aspx?sf=315428_Answer/6278071ec2473b5fd609c12cb1768387.gif" style="vertical-align:-7px" width="350"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="4.251178959*(-0.4917713136e-1+0.4030e-2*sigma)^2" height="30" src="/view.aspx?sf=315428_Answer/17337cc759bf64a62cd3e8dc1e954f36.gif" style="vertical-align:-7px" width="350"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=315428_Answer/cdca36b55e2842521b4a6abb20bb12be.gif" style="vertical-align:-7px" width="6"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="A1 := plot([P11, P21, P31], sigma = 0 .. .7, color = [&amp;quot;Red&amp;quot;, &amp;quot;Blue&amp;quot;, &amp;quot;Green&amp;quot;], labels = [sigma, `&amp;amp;pi;__m`], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;W&amp;quot;));`, `#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;D&amp;quot;));`, `#msubsup(mi(&amp;quot;&amp;amp;pi;&amp;quot;),mi(&amp;quot;n&amp;quot;),mn(&amp;quot;DS&amp;quot;));`], axis[2] = [color = &amp;quot;#600000&amp;quot;])" height="135" src="/view.aspx?sf=315428_Answer/fd9e3de19840f0d9d3ee2801009a2ed0.gif" style="vertical-align:-116px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="500" src="/view.aspx?sf=315428_Answer/e7684fcbdf20391409c835dd65542f2b.gif" style="border:none" width="500"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="display(A1, pointplot([[X, Y]], symbol = circle, symbolsize = 25, color = blue))" height="96" src="/view.aspx?sf=315428_Answer/b0f95216e278c10fb9a9e038cd5cc5c2.gif" style="vertical-align:-79px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;a href="http://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20(in%20plots%3A-pointplot)%20points%20cannot%20be%20converted%20to%20floating-point%20values"&gt;&lt;span style="color:#ff00ff;font-size: 100%;font-family: Courier New,monospace;font-weight:normal;font-style:normal;"&gt;&lt;u&gt;Error, (in plots:-pointplot) points cannot be converted to floating-point values&lt;/u&gt;&lt;/span&gt;&lt;/a&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=315428_Answer/d8e67d3762be39da27cdbdb65b664249.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=315428_Answer/Manf_profit__t_graph_changes_needed.mw"&gt;Download Manf_profit__t_graph_changes_needed.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>242188</guid>
      <pubDate>Thu, 22 Jan 2026 12:28:23 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
    <item>
      <title>Multiple plot overlay</title>
      <link>http://www.mapleprimes.com/questions/242016-Multiple-Plot-Overlay?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;Syntax for merging and overlaying all three graphs on a single plot.&lt;br&gt;
Include three sets of iso-profit lines on the same axes:&lt;br&gt;
&amp;ndash; Case 1: thin solid lines&lt;br&gt;
&amp;ndash; case 2: brown dashed lines&lt;br&gt;
&amp;ndash; Case 3: grey semi-dashed lines&lt;br&gt;
Also add vector arrows to show the direction of maximum profit increase.&lt;br&gt;
Combined plot = Plot 1 + Plot 2 +&amp;nbsp; Plot 3&lt;br&gt;
Attaching sheet:&lt;br&gt;
&lt;a href="/view.aspx?sf=242016_question/case_1.mw"&gt;case_1.mw&lt;/a&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;a href="/view.aspx?sf=242016_question/case_2.mw"&gt;case_2.mw&lt;/a&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;a href="/view.aspx?sf=242016_question/Case_3.mw"&gt;Case_3.mw&lt;/a&gt;&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;p&gt;sample graph:&amp;nbsp;&lt;img src="/view.aspx?sf=242016_question/sample.JPG"&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Syntax for merging and overlaying all three graphs on a single plot.&lt;br data-end="112" data-start="109"&gt;
Include three sets of iso-profit lines on the same axes:&lt;br data-end="171" data-start="168"&gt;
&amp;ndash; Case 1: thin solid lines&lt;br data-end="204" data-start="201"&gt;
&amp;ndash; case 2: brown dashed lines&lt;br data-end="239" data-start="236"&gt;
&amp;ndash; Case 3: grey semi-dashed lines&lt;br data-end="278" data-start="275"&gt;
Also add vector arrows to show the direction of maximum profit increase.&lt;br&gt;
Combined plot = Plot 1 + Plot 2 +&amp;nbsp; Plot 3&lt;br&gt;
Attaching sheet:&lt;br&gt;
&lt;a href="/view.aspx?sf=242016_question/case_1.mw"&gt;case_1.mw&lt;/a&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;a href="/view.aspx?sf=242016_question/case_2.mw"&gt;case_2.mw&lt;/a&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;a href="/view.aspx?sf=242016_question/Case_3.mw"&gt;Case_3.mw&lt;/a&gt;&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;p&gt;sample graph:&amp;nbsp;&lt;img src="/view.aspx?sf=242016_question/sample.JPG"&gt;&lt;/p&gt;
</description>
      <guid>242016</guid>
      <pubDate>Wed, 19 Nov 2025 16:21:00 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
    <item>
      <title>How to scale plots, to distinguish multiple curves?</title>
      <link>http://www.mapleprimes.com/questions/241994-How-To-Scale-Plots-To-Distinguish-Multiple?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;In the current graph, the three curves appear close together and are hard to distinguish because of a scaling issue. How can we adjust the scale so that each line is clearly visible and separate?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="31884F541F1390AB660662C02508570B"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241994_question/bb559a0b6fd4bf4166678658ef395f91.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="L1 := ((3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)-.35)*(3.000000000-(3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48))+(.9*(.5+(.6250000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)))*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))+.1408958333+(0.2430555555e-1*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)+0.207886905e-1)*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(3.000000000-(3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48))^2-(.1583333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48)+(.6200396825*(-.339960-(.5000000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)))*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)); L2 := ((3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48))+(.9*(.47+(.6250000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)))*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))+.1345516666+(0.2430555555e-1*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)+0.359077381e-1)*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48))^2-(.1583333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48)+(.6200396825*(-.364344-(.5000000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)))*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)); L3 := ((3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48))+(.9*(.47+(.6250000000*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)))*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))+.1344738889+(0.2430555555e-1*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)+0.369156746e-1)*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48))^2+(-.1949156746-(.3100198412*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))-(.1583333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48)" height="1844" src="/view.aspx?sf=241994_question/a8a65e214093cdbaedf23314bcf47a5e.gif" style="vertical-align:-1811px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)-.35)*(3.000000000-3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48))+.9*(.5+.6250000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))+.1408958333+0.2430555555e-1*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24)+0.207886905e-1)*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(3.000000000-3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48))^2-.1583333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)+.6200396825*(-.339960-.5000000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))" height="633" src="/view.aspx?sf=241994_question/c74f158531a570ce27ee156c5ae7329c.gif" style="vertical-align:-600px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48))+.9*(.47+.6250000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))+.1345516666+0.2430555555e-1*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24)+0.359077381e-1)*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48))^2-.1583333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)+.6200396825*(-.364344-.5000000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))" height="633" src="/view.aspx?sf=241994_question/bba040ea7e1b00ad95dae0186361a98d.gif" style="vertical-align:-600px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48))+.9*(.47+.6250000000*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))+.1344738889+0.2430555555e-1*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24)+0.369156746e-1)*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48))^2+(-.1949156746-.3100198412*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))-.1583333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)" height="640" src="/view.aspx?sf=241994_question/9b126dc08ffb02f4e0e56d3cd3c42b82.gif" style="vertical-align:-607px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="G2 := plot([L1, L2, L3], rho0 = 0 .. .8, color = [&amp;quot;#00FF00&amp;quot;, &amp;quot;#00BC00&amp;quot;, &amp;quot;#008000&amp;quot;], labels = [typeset(Typesetting:-mo(&amp;quot;&amp;amp;rho;&amp;quot;, mathvariant = &amp;quot;bold&amp;quot;), &amp;quot;\n&amp;quot;), typeset(&amp;quot;\n&amp;quot;, Typesetting:-mo(&amp;quot;Retailer profit&amp;quot;, mathvariant = &amp;quot;bold&amp;quot;, mathcolor = &amp;quot;black&amp;quot;))], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;W&amp;quot;));`, `#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`, `#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;S&amp;quot;));`], axis[2] = [color = &amp;quot;#006000&amp;quot;])" height="116" src="/view.aspx?sf=241994_question/f76bfad4d04746dd21723bc599d5171e.gif" style="vertical-align:-97px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241994_question/357f7e31cd66cdf0cc39214e8b89932f.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241994_question/f892f9c8f28fd8ef229a1cd9d37f8ede.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241994_question/Q_SEPERATE.mw"&gt;Download Q_SEPERATE.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;In the current graph, the three curves appear close together and are hard to distinguish because of a scaling issue. How can we adjust the scale so that each line is clearly visible and separate?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="31884F541F1390AB660662C02508570B"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241994_question/bb559a0b6fd4bf4166678658ef395f91.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="L1 := ((3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)-.35)*(3.000000000-(3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48))+(.9*(.5+(.6250000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)))*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))+.1408958333+(0.2430555555e-1*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)+0.207886905e-1)*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(3.000000000-(3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48))^2-(.1583333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000))/(3.6288*rho0^2+.48)+(.6200396825*(-.339960-(.5000000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)))*(0.163690476e-1-(.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1))/(1.8144*rho0^2+.24)); L2 := ((3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48))+(.9*(.47+(.6250000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)))*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))+.1345516666+(0.2430555555e-1*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)+0.359077381e-1)*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48))^2-(.1583333333*(3.14725824*rho0^2-.10491*rho0+.284952))/(3.6288*rho0^2+.48)+(.6200396825*(-.364344-(.5000000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)))*(0.282738095e-1-(.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1))/(1.8144*rho0^2+.24)); L3 := ((3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48))+(.9*(.47+(.6250000000*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)))*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))+.1344738889+(0.2430555555e-1*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)+(-(.3149801588*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24)+0.369156746e-1)*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-(3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48))^2+(-.1949156746-(.3100198412*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))*(0.290674603e-1-(.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1))/(1.8144*rho0^2+.24))-(.1583333333*(3.14725824*rho0^2-.105342*rho0+.284952))/(3.6288*rho0^2+.48)" height="1844" src="/view.aspx?sf=241994_question/a8a65e214093cdbaedf23314bcf47a5e.gif" style="vertical-align:-1811px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)-.35)*(3.000000000-3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48))+.9*(.5+.6250000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))+.1408958333+0.2430555555e-1*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24)+0.207886905e-1)*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(3.000000000-3.333333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48))^2-.1583333333*(3.26592*rho0^2-0.9411e-1*rho0+.3000)/(3.6288*rho0^2+.48)+.6200396825*(-.339960-.5000000000*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))*(0.163690476e-1-.2480158730*(-.5126688*rho0^2-.887040*rho0+0.1584e-1)/(1.8144*rho0^2+.24))" height="633" src="/view.aspx?sf=241994_question/c74f158531a570ce27ee156c5ae7329c.gif" style="vertical-align:-600px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48))+.9*(.47+.6250000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))+.1345516666+0.2430555555e-1*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24)+0.359077381e-1)*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-3.333333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48))^2-.1583333333*(3.14725824*rho0^2-.10491*rho0+.284952)/(3.6288*rho0^2+.48)+.6200396825*(-.364344-.5000000000*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))*(0.282738095e-1-.2480158730*(-.4981536*rho0^2-.88268544*rho0+0.2736e-1)/(1.8144*rho0^2+.24))" height="633" src="/view.aspx?sf=241994_question/bba040ea7e1b00ad95dae0186361a98d.gif" style="vertical-align:-600px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="((3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)-.32)*(2.891000000-3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48))+.9*(.47+.6250000000*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))+.1344738889+0.2430555555e-1*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24)+(-.3149801588*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24)+0.369156746e-1)*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))-0.1000000000e-1*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))^2+(1/2)*(2.891000000-3.333333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48))^2+(-.1949156746-.3100198412*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))*(0.290674603e-1-.2480158730*(-.49525056*rho0^2-.88268544*rho0+0.28128e-1)/(1.8144*rho0^2+.24))-.1583333333*(3.14725824*rho0^2-.105342*rho0+.284952)/(3.6288*rho0^2+.48)" height="640" src="/view.aspx?sf=241994_question/9b126dc08ffb02f4e0e56d3cd3c42b82.gif" style="vertical-align:-607px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="G2 := plot([L1, L2, L3], rho0 = 0 .. .8, color = [&amp;quot;#00FF00&amp;quot;, &amp;quot;#00BC00&amp;quot;, &amp;quot;#008000&amp;quot;], labels = [typeset(Typesetting:-mo(&amp;quot;&amp;amp;rho;&amp;quot;, mathvariant = &amp;quot;bold&amp;quot;), &amp;quot;\n&amp;quot;), typeset(&amp;quot;\n&amp;quot;, Typesetting:-mo(&amp;quot;Retailer profit&amp;quot;, mathvariant = &amp;quot;bold&amp;quot;, mathcolor = &amp;quot;black&amp;quot;))], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;W&amp;quot;));`, `#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`, `#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;S&amp;quot;));`], axis[2] = [color = &amp;quot;#006000&amp;quot;])" height="116" src="/view.aspx?sf=241994_question/f76bfad4d04746dd21723bc599d5171e.gif" style="vertical-align:-97px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241994_question/357f7e31cd66cdf0cc39214e8b89932f.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241994_question/f892f9c8f28fd8ef229a1cd9d37f8ede.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241994_question/Q_SEPERATE.mw"&gt;Download Q_SEPERATE.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>241994</guid>
      <pubDate>Sat, 15 Nov 2025 04:59:43 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
    <item>
      <title>syntax error using union</title>
      <link>http://www.mapleprimes.com/questions/241983-Syntax-Error-Using-Union?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;I&amp;#39;m getting an error while executing the for loop after adding a constraint. Could you please help me identify and fix the syntax issue?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="8BB6B18D025ABB89DBB5CC0AFED0A68A"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241983_question/4b5775678d29f4e257f9fe2b5c51249c.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#666699;font-size: 100%;font-family: Courier New,monospace;background-color: #ccffff;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="C1 := (Cr*Pr*d*rho0-Cr*d*delta*rho0+Ce*d*delta+Cr*d*rho0-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*rho0+a*delta+c*d-d*w-2*delta*rho0+g*i2-a+2*rho0)/(rho0*(Cr*d+2)) &amp;lt;= Pn; C11 := Pn &amp;lt;= (Cr*Pr*d*upsilon-Cr*d*delta*upsilon+Ce*d*delta+Cr*d*upsilon-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*upsilon+a*delta+c*d-d*w-2*delta*upsilon+g*i2-a+2*upsilon)/(upsilon*(Cr*d+2))" height="141" src="/view.aspx?sf=241983_question/489613566791a23ad60dbfeb2c96b2b1.gif" style="vertical-align:-115px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Cr*Pr*d*rho0-Cr*d*delta*rho0+Ce*d*delta+Cr*d*rho0-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*rho0+a*delta+c*d-d*w-2*delta*rho0+g*i2-a+2*rho0)/(rho0*(Cr*d+2)) &amp;lt;= Pn" height="65" src="/view.aspx?sf=241983_question/cd083fbcb8d3c43ddc29f36bdfe9c619.gif" style="vertical-align:-39px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="Pn &amp;lt;= (Cr*Pr*d*upsilon-Cr*d*delta*upsilon+Ce*d*delta+Cr*d*upsilon-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*upsilon+a*delta+c*d-d*w-2*delta*upsilon+g*i2-a+2*upsilon)/(upsilon*(Cr*d+2))" height="65" src="/view.aspx?sf=241983_question/41bc6717333a5f116efa12b56811510e.gif" style="vertical-align:-39px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;m` := (Pn-Cn)*(1-(Pn-Pr)/(1-delta))+(Pr-w-Crm)*alpha*((((-a+0.4e-1*g)*Cr-c-(0.6e-1*alpha*d*rho0^2+2*d*delta*rho0-2*Pr*d*rho0+2*alpha*c*rho0^2-0.8e-1*alpha*g*rho0^2-2*a*d*delta+2*c*d^2*delta+2*Cn*d*rho0+0.3e-1*Cr*d^2*rho0^2-Cr*d^2*rho0+0.8e-1*d*delta*g+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+2*a*d-2*c*d^2)/(2*d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)-0.4e-1*g+a)-(0.3e-1*(((-a+0.4e-1*g)*Cr-c-(0.6e-1*alpha*d*rho0^2+2*d*delta*rho0-2*Pr*d*rho0+2*alpha*c*rho0^2-0.8e-1*alpha*g*rho0^2-2*a*d*delta+2*c*d^2*delta+2*Cn*d*rho0+0.3e-1*Cr*d^2*rho0^2-Cr*d^2*rho0+0.8e-1*d*delta*g+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+2*a*d-2*c*d^2)/(2*d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a))/(Cr*d+2)+0.12e-2*g-0.3e-1*a" height="303" src="/view.aspx?sf=241983_question/417a5be18c5663a6caaa7474379fddf6.gif" style="vertical-align:-277px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Pn-Cn)*(1-(Pn-Pr)/(1-delta))+(Pr-w-Crm)*alpha*((((-a+0.4e-1*g)*Cr-c-(1/2)*(-0.8e-1*alpha*g*rho0^2+2*alpha*c*rho0^2+0.8e-1*d*delta*g+2*c*d^2*delta+0.6e-1*alpha*d*rho0^2-2*a*d*delta-Cr*d^2*rho0+0.3e-1*Cr*d^2*rho0^2+2*d*delta*rho0+2*Cn*d*rho0-2*Pr*d*rho0+2*a*d-2*c*d^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2)/(d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)-0.4e-1*g+a)-0.3e-1*(((-a+0.4e-1*g)*Cr-c-(1/2)*(-0.8e-1*alpha*g*rho0^2+2*alpha*c*rho0^2+0.8e-1*d*delta*g+2*c*d^2*delta+0.6e-1*alpha*d*rho0^2-2*a*d*delta-Cr*d^2*rho0+0.3e-1*Cr*d^2*rho0^2+2*d*delta*rho0+2*Cn*d*rho0-2*Pr*d*rho0+2*a*d-2*c*d^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2)/(d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)+0.12e-2*g-0.3e-1*a" height="303" src="/view.aspx?sf=241983_question/bdb91b9623985aabc2a0f00b1c0a91bb.gif" style="vertical-align:-277px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="DATA := [delta = .7, a = .2, d = .9, g = .3, c = 0.2e-1, sigma = .5, Cn = .35, Crm = .1, Cr = 0.1e-1, rho0 = .4, Pr = .6, alpha = .9, s = .21, upsilon = .95]" height="46" src="/view.aspx?sf=241983_question/b221613a727ee4dcfde14b48be8ede50.gif" style="vertical-align:-27px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="TRC := proc (Pn, w) options operator, arrow; eval(`&amp;amp;Pi;m`, DATA) end proc; C2 := subs(DATA, C1); C22 := subs(DATA, C11)" height="43" src="/view.aspx?sf=241983_question/ccbb0f30f2f81c93595427589a4b6808.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-.3359880537*Ce+.1119960179*i2-.3359880537*w+.8320557491 &amp;lt;= Pn" height="23" src="/view.aspx?sf=241983_question/7d9a5750cc65e965725a2013ed372e3c.gif" style="vertical-align:-6px" width="545"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pn &amp;lt;= -.1414686542*Ce+0.4715621807e-1*i2-.1414686542*w+.8713918944" height="23" src="/view.aspx?sf=241983_question/b2203ac868ca195f1f1e084221715900.gif" style="vertical-align:-6px" width="560"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="C3 := isolate(C2, w); C33 := isolate(C22, w)" height="23" src="/view.aspx?sf=241983_question/ea8c37cbcd77112490e2df95ad265ed5.gif" style="vertical-align:-6px" width="298"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-.3359880537*w &amp;lt;= Pn+.3359880537*Ce-.1119960179*i2-.8320557491" height="23" src="/view.aspx?sf=241983_question/882be25bd5250e65dce93cc62c1e3157.gif" style="vertical-align:-6px" width="545"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="w &amp;lt;= 6.159611112-7.068703704*Pn-.9999999999*Ce+.3333333333*i2" height="23" src="/view.aspx?sf=241983_question/147d0d523f5aecc6eeeff466b71c7415.gif" style="vertical-align:-6px" width="527"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="t := {0.3e-1, 0.5e-1, 0.7e-1, 0.9e-1}; ts := {0.4e-1, 0.8e-1, .12}" height="23" src="/view.aspx?sf=241983_question/f3b90810876878bb48089a2a63833ae7.gif" style="vertical-align:-6px" width="345"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M := Matrix(nops(t)*nops(ts), 3); rr := 0; for Ce in t do for i2 in ts do C4 := eval(C3, [Ce = t, i2 = ts]); C44 := eval(C33, [Ce = t, i2 = ts]); s := Optimization:-Maximize(TRC(Pn, w), `union`(C4, C44), Pn = 0 .. 1, w = 0 .. 1, assume = nonnegative); stemp := s[1]; Pntemp := s[2][1]; wtemp := s[2][2]; rr := rr+1; M[rr, 1 .. 3] := `&amp;lt;|&amp;gt;`(Ce, i2, stemp); print(Ce, i2, stemp, Pntemp, wtemp) end do end do" height="212" src="/view.aspx?sf=241983_question/247987176e518eb4bb290c090a1a26e6.gif" style="vertical-align:-195px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;a href="http://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20invalid%20input%3A%20%60union%60%20received%20-.3359880537*w%20%3C%3D%20Pn-.8264559482,%20which%20is%20not%20valid%20for%20its%201st%20argument"&gt;&lt;span style="color:#ff00ff;font-size: 100%;font-family: Courier New,monospace;font-weight:normal;font-style:normal;"&gt;&lt;u&gt;Error, invalid input: `union` received -.3359880537*w &amp;lt;= Pn-.8264559482, which is not valid for its 1st argument&lt;/u&gt;&lt;/span&gt;&lt;/a&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;R := Array(ArrayTools:-Reshape(M,[3,4,3]),datatype=float[8]):&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;func := Interpolation:-SplineInterpolation([[0.04, 0.08, 0.12],[0.03, 0.05, 0.07, 0.09]],R[..,..,3]):&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;conts := [seq(min(R[..,..,3])..max(R[..,..,3]),(max(R[..,..,3])-min(R[..,..,3]))/8)];&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[HFloat(0.0)]" height="23" src="/view.aspx?sf=241983_question/4b33a77cd022b7d0d275df53c32ce661.gif" style="vertical-align:-6px" width="87"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241983_question/832c6f7299d84b7feaaf2bf62aea94b9.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;span name="eccodeeditgroup83_body"&gt;&lt;span name="eccodeedit84_control"&gt;&lt;input align="center" height="40" name="eccodeedit84_control_button" src="/view.aspx?sf=241983_question/c315e8e317a5ad4e466c8420077eb7dd.gif" type="image" width="40"&gt;&lt;/span&gt;&lt;span&gt;ContoursWithLabels:= proc(&lt;/span&gt; &lt;/span&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="ContoursWithLabels(func(x, y), x = 0.3e-1 .. .15, y = 0.2e-1 .. .1, contours = conts, decplaces = 4, Coloring = [colorstyle = HUE, colorscheme = [&amp;quot;Blue&amp;quot;, &amp;quot;Gold&amp;quot;], style = surface], TextOptions = [font = [HELVETICA, BOLD, 9], color = black], GraphicOptions = [thickness = 0], ImplicitplotOptions = [gridrefine = 3], size = [700, 600], labels = [':-C__e', ':-i__2'])" height="138" src="/view.aspx?sf=241983_question/cbaee5f4c682e88ac36c85ac5a2bcafe.gif" style="vertical-align:-121px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241983_question/Q_Constraint_error.mw"&gt;Download Q_Constraint_error.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I&amp;#39;m getting an error while executing the for loop after adding a constraint. Could you please help me identify and fix the syntax issue?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="8BB6B18D025ABB89DBB5CC0AFED0A68A"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241983_question/4b5775678d29f4e257f9fe2b5c51249c.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#666699;font-size: 100%;font-family: Courier New,monospace;background-color: #ccffff;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="C1 := (Cr*Pr*d*rho0-Cr*d*delta*rho0+Ce*d*delta+Cr*d*rho0-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*rho0+a*delta+c*d-d*w-2*delta*rho0+g*i2-a+2*rho0)/(rho0*(Cr*d+2)) &amp;lt;= Pn; C11 := Pn &amp;lt;= (Cr*Pr*d*upsilon-Cr*d*delta*upsilon+Ce*d*delta+Cr*d*upsilon-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*upsilon+a*delta+c*d-d*w-2*delta*upsilon+g*i2-a+2*upsilon)/(upsilon*(Cr*d+2))" height="141" src="/view.aspx?sf=241983_question/489613566791a23ad60dbfeb2c96b2b1.gif" style="vertical-align:-115px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Cr*Pr*d*rho0-Cr*d*delta*rho0+Ce*d*delta+Cr*d*rho0-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*rho0+a*delta+c*d-d*w-2*delta*rho0+g*i2-a+2*rho0)/(rho0*(Cr*d+2)) &amp;lt;= Pn" height="65" src="/view.aspx?sf=241983_question/cd083fbcb8d3c43ddc29f36bdfe9c619.gif" style="vertical-align:-39px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="Pn &amp;lt;= (Cr*Pr*d*upsilon-Cr*d*delta*upsilon+Ce*d*delta+Cr*d*upsilon-c*d*delta+d*delta*w-delta*g*i2-Ce*d+2*Pr*upsilon+a*delta+c*d-d*w-2*delta*upsilon+g*i2-a+2*upsilon)/(upsilon*(Cr*d+2))" height="65" src="/view.aspx?sf=241983_question/41bc6717333a5f116efa12b56811510e.gif" style="vertical-align:-39px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;m` := (Pn-Cn)*(1-(Pn-Pr)/(1-delta))+(Pr-w-Crm)*alpha*((((-a+0.4e-1*g)*Cr-c-(0.6e-1*alpha*d*rho0^2+2*d*delta*rho0-2*Pr*d*rho0+2*alpha*c*rho0^2-0.8e-1*alpha*g*rho0^2-2*a*d*delta+2*c*d^2*delta+2*Cn*d*rho0+0.3e-1*Cr*d^2*rho0^2-Cr*d^2*rho0+0.8e-1*d*delta*g+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+2*a*d-2*c*d^2)/(2*d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)-0.4e-1*g+a)-(0.3e-1*(((-a+0.4e-1*g)*Cr-c-(0.6e-1*alpha*d*rho0^2+2*d*delta*rho0-2*Pr*d*rho0+2*alpha*c*rho0^2-0.8e-1*alpha*g*rho0^2-2*a*d*delta+2*c*d^2*delta+2*Cn*d*rho0+0.3e-1*Cr*d^2*rho0^2-Cr*d^2*rho0+0.8e-1*d*delta*g+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+2*a*d-2*c*d^2)/(2*d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a))/(Cr*d+2)+0.12e-2*g-0.3e-1*a" height="303" src="/view.aspx?sf=241983_question/417a5be18c5663a6caaa7474379fddf6.gif" style="vertical-align:-277px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(Pn-Cn)*(1-(Pn-Pr)/(1-delta))+(Pr-w-Crm)*alpha*((((-a+0.4e-1*g)*Cr-c-(1/2)*(-0.8e-1*alpha*g*rho0^2+2*alpha*c*rho0^2+0.8e-1*d*delta*g+2*c*d^2*delta+0.6e-1*alpha*d*rho0^2-2*a*d*delta-Cr*d^2*rho0+0.3e-1*Cr*d^2*rho0^2+2*d*delta*rho0+2*Cn*d*rho0-2*Pr*d*rho0+2*a*d-2*c*d^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2)/(d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)-0.4e-1*g+a)-0.3e-1*(((-a+0.4e-1*g)*Cr-c-(1/2)*(-0.8e-1*alpha*g*rho0^2+2*alpha*c*rho0^2+0.8e-1*d*delta*g+2*c*d^2*delta+0.6e-1*alpha*d*rho0^2-2*a*d*delta-Cr*d^2*rho0+0.3e-1*Cr*d^2*rho0^2+2*d*delta*rho0+2*Cn*d*rho0-2*Pr*d*rho0+2*a*d-2*c*d^2-0.6e-1*d^2*delta+0.6e-1*d*rho0^2-0.8e-1*d*g-2*d*rho0+0.6e-1*d^2+0.3e-1*Cr*alpha*d^2*rho0^2+Cn*Cr*d^2*rho0-Cr*Pr*d^2*rho0+Cr*d^2*delta*rho0+2*Crm*alpha*d*rho0^2-2*Pr*alpha*d*rho0^2-2*alpha*c*d*rho0^2+Cr*Crm*alpha*d^2*rho0^2-Cr*Pr*alpha*d^2*rho0^2-Cr*alpha*c*d^2*rho0^2+Cr*alpha*c*d*rho0^2-0.4e-1*Cr*alpha*d*g*rho0^2)/(d*(Cr*alpha*d*rho0^2+2*alpha*rho0^2-d*delta+d))+0.3e-1)*d+0.4e-1*g-a)/(Cr*d+2)+0.12e-2*g-0.3e-1*a" height="303" src="/view.aspx?sf=241983_question/bdb91b9623985aabc2a0f00b1c0a91bb.gif" style="vertical-align:-277px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="DATA := [delta = .7, a = .2, d = .9, g = .3, c = 0.2e-1, sigma = .5, Cn = .35, Crm = .1, Cr = 0.1e-1, rho0 = .4, Pr = .6, alpha = .9, s = .21, upsilon = .95]" height="46" src="/view.aspx?sf=241983_question/b221613a727ee4dcfde14b48be8ede50.gif" style="vertical-align:-27px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="TRC := proc (Pn, w) options operator, arrow; eval(`&amp;amp;Pi;m`, DATA) end proc; C2 := subs(DATA, C1); C22 := subs(DATA, C11)" height="43" src="/view.aspx?sf=241983_question/ccbb0f30f2f81c93595427589a4b6808.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-.3359880537*Ce+.1119960179*i2-.3359880537*w+.8320557491 &amp;lt;= Pn" height="23" src="/view.aspx?sf=241983_question/7d9a5750cc65e965725a2013ed372e3c.gif" style="vertical-align:-6px" width="545"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pn &amp;lt;= -.1414686542*Ce+0.4715621807e-1*i2-.1414686542*w+.8713918944" height="23" src="/view.aspx?sf=241983_question/b2203ac868ca195f1f1e084221715900.gif" style="vertical-align:-6px" width="560"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="C3 := isolate(C2, w); C33 := isolate(C22, w)" height="23" src="/view.aspx?sf=241983_question/ea8c37cbcd77112490e2df95ad265ed5.gif" style="vertical-align:-6px" width="298"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-.3359880537*w &amp;lt;= Pn+.3359880537*Ce-.1119960179*i2-.8320557491" height="23" src="/view.aspx?sf=241983_question/882be25bd5250e65dce93cc62c1e3157.gif" style="vertical-align:-6px" width="545"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="w &amp;lt;= 6.159611112-7.068703704*Pn-.9999999999*Ce+.3333333333*i2" height="23" src="/view.aspx?sf=241983_question/147d0d523f5aecc6eeeff466b71c7415.gif" style="vertical-align:-6px" width="527"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="t := {0.3e-1, 0.5e-1, 0.7e-1, 0.9e-1}; ts := {0.4e-1, 0.8e-1, .12}" height="23" src="/view.aspx?sf=241983_question/f3b90810876878bb48089a2a63833ae7.gif" style="vertical-align:-6px" width="345"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="M := Matrix(nops(t)*nops(ts), 3); rr := 0; for Ce in t do for i2 in ts do C4 := eval(C3, [Ce = t, i2 = ts]); C44 := eval(C33, [Ce = t, i2 = ts]); s := Optimization:-Maximize(TRC(Pn, w), `union`(C4, C44), Pn = 0 .. 1, w = 0 .. 1, assume = nonnegative); stemp := s[1]; Pntemp := s[2][1]; wtemp := s[2][2]; rr := rr+1; M[rr, 1 .. 3] := `&amp;lt;|&amp;gt;`(Ce, i2, stemp); print(Ce, i2, stemp, Pntemp, wtemp) end do end do" height="212" src="/view.aspx?sf=241983_question/247987176e518eb4bb290c090a1a26e6.gif" style="vertical-align:-195px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;a href="http://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20invalid%20input%3A%20%60union%60%20received%20-.3359880537*w%20%3C%3D%20Pn-.8264559482,%20which%20is%20not%20valid%20for%20its%201st%20argument"&gt;&lt;span style="color:#ff00ff;font-size: 100%;font-family: Courier New,monospace;font-weight:normal;font-style:normal;"&gt;&lt;u&gt;Error, invalid input: `union` received -.3359880537*w &amp;lt;= Pn-.8264559482, which is not valid for its 1st argument&lt;/u&gt;&lt;/span&gt;&lt;/a&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;R := Array(ArrayTools:-Reshape(M,[3,4,3]),datatype=float[8]):&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;func := Interpolation:-SplineInterpolation([[0.04, 0.08, 0.12],[0.03, 0.05, 0.07, 0.09]],R[..,..,3]):&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;conts := [seq(min(R[..,..,3])..max(R[..,..,3]),(max(R[..,..,3])-min(R[..,..,3]))/8)];&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[HFloat(0.0)]" height="23" src="/view.aspx?sf=241983_question/4b33a77cd022b7d0d275df53c32ce661.gif" style="vertical-align:-6px" width="87"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241983_question/832c6f7299d84b7feaaf2bf62aea94b9.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;span name="eccodeeditgroup83_body"&gt;&lt;span name="eccodeedit84_control"&gt;&lt;input align="center" height="40" name="eccodeedit84_control_button" src="/view.aspx?sf=241983_question/c315e8e317a5ad4e466c8420077eb7dd.gif" type="image" width="40"&gt;&lt;/span&gt;&lt;span&gt;ContoursWithLabels:= proc(&lt;/span&gt; &lt;/span&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="ContoursWithLabels(func(x, y), x = 0.3e-1 .. .15, y = 0.2e-1 .. .1, contours = conts, decplaces = 4, Coloring = [colorstyle = HUE, colorscheme = [&amp;quot;Blue&amp;quot;, &amp;quot;Gold&amp;quot;], style = surface], TextOptions = [font = [HELVETICA, BOLD, 9], color = black], GraphicOptions = [thickness = 0], ImplicitplotOptions = [gridrefine = 3], size = [700, 600], labels = [':-C__e', ':-i__2'])" height="138" src="/view.aspx?sf=241983_question/cbaee5f4c682e88ac36c85ac5a2bcafe.gif" style="vertical-align:-121px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241983_question/Q_Constraint_error.mw"&gt;Download Q_Constraint_error.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>241983</guid>
      <pubDate>Wed, 12 Nov 2025 12:07:09 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
    <item>
      <title>2D plot of multiple inequalities or maximum</title>
      <link>http://www.mapleprimes.com/questions/241979-2D-Plot-Of-Multiple-Inequalities-Or-Maximum?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;I currently have a 3D plot where the axes are Pn​, w, and the objective value (TM1, TM2, TM3 are all positive). I want to convert this into a 2D regional plot with Pn on the x-axis and w on the y-axis. How do I write the syntax for generating such a 2D region plot?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="D46AEC2030999D08919721D5046170D0"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241979_question/9b5e3613982e4bc1391200a51e67edff.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="with(Optimization); with(plots); with(LinearAlgebra)" height="57" src="/view.aspx?sf=241979_question/9d528e302e9483d617e2614b9f48552f.gif" style="vertical-align:-40px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=241979_question/436204b6254d294d697e25724eb97586.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=241979_question/36c9854f196e7b45a92165696c876a52.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM1 := (Pn-.35)*(3.000000000-3.333333333*Pn)+.1115859938-.2510684861*w" height="23" src="/view.aspx?sf=241979_question/5d8efb295312b9644a18e153240435e7.gif" style="vertical-align:-6px" width="581"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.35)*(3.000000000-3.333333333*Pn)+.1115859938-.2510684861*w" height="23" src="/view.aspx?sf=241979_question/0d7d724868f2bf545ca9402d2e4142e2.gif" style="vertical-align:-6px" width="573"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM2 := (Pn-.348)*(2.996666666-3.333333333*Pn)+.1017286174-.2299240474*w" height="23" src="/view.aspx?sf=241979_question/ec22502990e47fa1b96f3adae812d422.gif" style="vertical-align:-6px" width="588"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.348)*(2.996666666-3.333333333*Pn)+.1017286174-.2299240474*w" height="23" src="/view.aspx?sf=241979_question/f4a5e5480a7f68a0ce8f74b17a0d4b2b.gif" style="vertical-align:-6px" width="580"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM3 := (Pn-.348)*(2.996666666-3.333333333*Pn)+.1018208882-.2301325952*w" height="23" src="/view.aspx?sf=241979_question/cf50b3e356bb9261e06aa7de2f71f7a9.gif" style="vertical-align:-6px" width="588"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.348)*(2.996666666-3.333333333*Pn)+.1018208882-.2301325952*w" height="23" src="/view.aspx?sf=241979_question/861d63f92c421fe1a312fedd611b1cb3.gif" style="vertical-align:-6px" width="580"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S1 := plot3d(TM1, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;SkyBlue&amp;quot;); S2 := plot3d(TM2, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;Yellow&amp;quot;); S3 := plot3d(TM3, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;Red&amp;quot;)" height="78" src="/view.aspx?sf=241979_question/80864fc1a86ea4b2950a063a51ffcc80.gif" style="vertical-align:-61px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="display({S1, S2, S3})" height="23" src="/view.aspx?sf=241979_question/8b837deab9effbbea8f1a156c43f9c47.gif" style="vertical-align:-6px" width="145"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="398" src="/view.aspx?sf=241979_question/dcb4ff47a9cb5d07b936dc2c9c8a1275.gif" style="border:none" width="510"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241979_question/14c487353dea19b6ceac75731692973a.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241979_question/Plot_3D_to_2D.mw"&gt;Download Plot_3D_to_2D.mw&lt;/a&gt;&lt;/p&gt;

&lt;form name="worksheet_form"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;&amp;nbsp;&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;img src="/view.aspx?sf=241979_question/rEGIONAL.JPG"&gt;&lt;/form&gt;
</itunes:summary>
      <description>&lt;p&gt;I currently have a 3D plot where the axes are Pn​, w, and the objective value (TM1, TM2, TM3 are all positive). I want to convert this into a 2D regional plot with Pn on the x-axis and w on the y-axis. How do I write the syntax for generating such a 2D region plot?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="D46AEC2030999D08919721D5046170D0"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241979_question/9b5e3613982e4bc1391200a51e67edff.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="with(Optimization); with(plots); with(LinearAlgebra)" height="57" src="/view.aspx?sf=241979_question/9d528e302e9483d617e2614b9f48552f.gif" style="vertical-align:-40px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=241979_question/436204b6254d294d697e25724eb97586.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=241979_question/36c9854f196e7b45a92165696c876a52.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&amp;nbsp;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM1 := (Pn-.35)*(3.000000000-3.333333333*Pn)+.1115859938-.2510684861*w" height="23" src="/view.aspx?sf=241979_question/5d8efb295312b9644a18e153240435e7.gif" style="vertical-align:-6px" width="581"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.35)*(3.000000000-3.333333333*Pn)+.1115859938-.2510684861*w" height="23" src="/view.aspx?sf=241979_question/0d7d724868f2bf545ca9402d2e4142e2.gif" style="vertical-align:-6px" width="573"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM2 := (Pn-.348)*(2.996666666-3.333333333*Pn)+.1017286174-.2299240474*w" height="23" src="/view.aspx?sf=241979_question/ec22502990e47fa1b96f3adae812d422.gif" style="vertical-align:-6px" width="588"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.348)*(2.996666666-3.333333333*Pn)+.1017286174-.2299240474*w" height="23" src="/view.aspx?sf=241979_question/f4a5e5480a7f68a0ce8f74b17a0d4b2b.gif" style="vertical-align:-6px" width="580"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="TM3 := (Pn-.348)*(2.996666666-3.333333333*Pn)+.1018208882-.2301325952*w" height="23" src="/view.aspx?sf=241979_question/cf50b3e356bb9261e06aa7de2f71f7a9.gif" style="vertical-align:-6px" width="588"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(Pn-.348)*(2.996666666-3.333333333*Pn)+.1018208882-.2301325952*w" height="23" src="/view.aspx?sf=241979_question/861d63f92c421fe1a312fedd611b1cb3.gif" style="vertical-align:-6px" width="580"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S1 := plot3d(TM1, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;SkyBlue&amp;quot;); S2 := plot3d(TM2, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;Yellow&amp;quot;); S3 := plot3d(TM3, Pn = 0 .. 1, w = 0 .. 1, orientation = [165, 75, 0], color = &amp;quot;Red&amp;quot;)" height="78" src="/view.aspx?sf=241979_question/80864fc1a86ea4b2950a063a51ffcc80.gif" style="vertical-align:-61px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="display({S1, S2, S3})" height="23" src="/view.aspx?sf=241979_question/8b837deab9effbbea8f1a156c43f9c47.gif" style="vertical-align:-6px" width="145"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="398" src="/view.aspx?sf=241979_question/dcb4ff47a9cb5d07b936dc2c9c8a1275.gif" style="border:none" width="510"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241979_question/14c487353dea19b6ceac75731692973a.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241979_question/Plot_3D_to_2D.mw"&gt;Download Plot_3D_to_2D.mw&lt;/a&gt;&lt;/p&gt;

&lt;form name="worksheet_form"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;&amp;nbsp;&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;img src="/view.aspx?sf=241979_question/rEGIONAL.JPG"&gt;&lt;/form&gt;
</description>
      <guid>241979</guid>
      <pubDate>Tue, 11 Nov 2025 07:07:39 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
    <item>
      <title>Multiple curves in a dual-axis plot </title>
      <link>http://www.mapleprimes.com/questions/241972-Multiple-Curves-In-A-Dualaxis-Plot-?ref=Feed:MaplePrimes:Version Maple 2019</link>
      <itunes:summary>&lt;p&gt;I would like to combine all the plots into a single figure. The curves S1, S2, and S3 represent the manufacturer&amp;rsquo;s profit as Ce​ varies, and S12, S22, and S33 represent the retailer&amp;rsquo;s profit for the same changes in Ce​. I want all of these displayed together in one plot using a dual y-axis: one axis for the manufacturer&amp;rsquo;s profit and the other for the retailer&amp;rsquo;s profit, with Ce on the x-axis. How to create such a dual-axis plot &lt;strong&gt;with appropriate scaling&lt;/strong&gt; so that the differences between the curves are also clearly visible.&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="B398FDB4FB29D18CE6D4052A6DD6862D"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241972_question/e71ad89dd962ff0d11da17f034db6a4c.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)" height="23" src="/view.aspx?sf=241972_question/95b84f50a9a92e386607e7ef8c5d5634.gif" style="vertical-align:-6px" width="556"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241972_question/3db05e391e46cab98b223a8a07d843bc.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=241972_question/e3cc8c57d16a87ccbf9f4129244454a9.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=241972_question/28e03e65369fe32756b2e449c03a36a6.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_12` := (0.1455251030e-2*Ce+.5352049476)*(0.369876310e-1-0.3638127575e-2*Ce)+(.8*(-.1671790360+1.121361872*Ce))*(0.1849381518e-1-0.1819063782e-2*Ce)-Ce*(0.1849381518e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/e8d58cc58141964336fae8d8952e30cd.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5352049476)*(0.369876310e-1-0.3638127575e-2*Ce)+(-.1337432288+.8970894976*Ce)*(0.1849381518e-1-0.1819063782e-2*Ce)-Ce*(0.1849381518e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/111e7175e19ac17553cb42474aec67cc.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_22` := (0.1455251030e-2*Ce+.5356096675)*(0.355258312e-1-0.3638127575e-2*Ce)+(.8*(-.1184158360+1.121361872*Ce))*(0.1776291535e-1-0.1819063782e-2*Ce)-Ce*(0.1776291535e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/fda5161784fa985e4c03b6001792a841.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5356096675)*(0.355258312e-1-0.3638127575e-2*Ce)+(-0.9473266880e-1+.8970894976*Ce)*(0.1776291535e-1-0.1819063782e-2*Ce)-Ce*(0.1776291535e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/859d1f57b125b1f2f441864466b72190.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_32` := (0.1455251030e-2*Ce+.5356038465)*(0.355403838e-1-0.3638127575e-2*Ce)+(.8*(-.1179012835+1.121361872*Ce))*(0.1777019161e-1-0.1819063782e-2*Ce)-Ce*(0.1777019161e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/f6b9afd44ddab16b192f3f82420397ed.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5356038465)*(0.355403838e-1-0.3638127575e-2*Ce)+(-0.9432102680e-1+.8970894976*Ce)*(0.1777019161e-1-0.1819063782e-2*Ce)-Ce*(0.1777019161e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/e61df1afc69eed9033124f6f5e20a009.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S12 := plot(`&amp;amp;Pi;_12`, Ce = 0 .. 0.9e-1, color = [red], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer Profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;W&amp;quot;));`]); S22 := plot(`&amp;amp;Pi;_22`, Ce = 0 .. 0.9e-1, color = [green], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;D&amp;quot;));`]); S32 := plot(`&amp;amp;Pi;_32`, Ce = 0 .. 0.9e-1, color = [blue], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;S&amp;quot;));`])" height="106" src="/view.aspx?sf=241972_question/d63d30fa552b4284847f8def67ee3477.gif" style="vertical-align:-87px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/3b4bf557adf9fdb20c746a4387b6ffa1.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/a361c6f163856a09e6ff6f5993f94515.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/9f6a25a20f58af53743c9eccf56fa465.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_1` := (-0.60726413e-1*Ce+.6173851967)*(0.1849381518e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1849381518e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/867651a524b8d986d45dd59abef6fc8b.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.6173851967)*(0.1849381518e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1849381518e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/ca47d303080a1416682439c056736698.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_2` := (-0.60726413e-1*Ce+.5929853242)*(0.1776291535e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1776291535e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/20543c34700a6e0dc5b6e875f21ec38f.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.5929853242)*(0.1776291535e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1776291535e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/667cc56b27c1e32cc5229e3bfa24dccd.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_3` := (-0.60726413e-1*Ce+.5932282299)*(0.1777019161e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1777019161e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/339fcff31edbf4f205e7257350a1597b.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.5932282299)*(0.1777019161e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1777019161e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/868ff5001322e9db4611bc71a25712bc.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S1 := plot(`&amp;amp;Pi;_1`, Ce = 0 .. 0.9e-1, color = [yellow], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;W&amp;quot;));`]); S2 := plot(`&amp;amp;Pi;_2`, Ce = 0 .. 0.9e-1, color = [black], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer  profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`]); S3 := plot(`&amp;amp;Pi;_3`, Ce = 0 .. 0.9e-1, color = [grey], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;S&amp;quot;));`])" height="106" src="/view.aspx?sf=241972_question/9eca2e4620324f7ec9c0a00b040c6e15.gif" style="vertical-align:-87px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/5ab1ca265166b47f3a6c3c0553f24b6c.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/82f729995cd77c6e2faebd8cf2abd9d3.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/78d6747a3b0c0858e0d03aaff43694f8.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="dualaxisplot(plot(`&amp;amp;Pi;_22`, Ce = 0 .. 0.9e-1, color = [&amp;quot;red&amp;quot;], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;D&amp;quot;));`]), plot(`&amp;amp;Pi;_2`, Ce = 0 .. 0.9e-1, color = [&amp;quot;green&amp;quot;], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`]), title = &amp;quot;fairnes cost Comparison&amp;quot;)" height="86" src="/view.aspx?sf=241972_question/6d57b836614ebe9cb2531071793ba4c8.gif" style="vertical-align:-67px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/3c1ee4cb8a0e17edc91d7da30d850a29.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="display({S1, S12, S2, S22, S3, S32})" height="23" src="/view.aspx?sf=241972_question/6bdb47227635e872f6826e4bdde67a72.gif" style="vertical-align:-6px" width="232"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/18e040119b17e6033353ef105a544da3.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241972_question/05e23dd6819bc4b7b01ac683ba789d03.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241972_question/All_plots_Combined.mw"&gt;Download All_plots_Combined.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I would like to combine all the plots into a single figure. The curves S1, S2, and S3 represent the manufacturer&amp;rsquo;s profit as Ce​ varies, and S12, S22, and S33 represent the retailer&amp;rsquo;s profit for the same changes in Ce​. I want all of these displayed together in one plot using a dual y-axis: one axis for the manufacturer&amp;rsquo;s profit and the other for the retailer&amp;rsquo;s profit, with Ce on the x-axis. How to create such a dual-axis plot &lt;strong data-end="605" data-start="577"&gt;with appropriate scaling&lt;/strong&gt; so that the differences between the curves are also clearly visible.&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="B398FDB4FB29D18CE6D4052A6DD6862D"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=241972_question/e71ad89dd962ff0d11da17f034db6a4c.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)" height="23" src="/view.aspx?sf=241972_question/95b84f50a9a92e386607e7ef8c5d5634.gif" style="vertical-align:-6px" width="556"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241972_question/3db05e391e46cab98b223a8a07d843bc.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="_local(Pi)" height="23" src="/view.aspx?sf=241972_question/e3cc8c57d16a87ccbf9f4129244454a9.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Pi" height="26" src="/view.aspx?sf=241972_question/28e03e65369fe32756b2e449c03a36a6.gif" style="vertical-align:-7px" width="14"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_12` := (0.1455251030e-2*Ce+.5352049476)*(0.369876310e-1-0.3638127575e-2*Ce)+(.8*(-.1671790360+1.121361872*Ce))*(0.1849381518e-1-0.1819063782e-2*Ce)-Ce*(0.1849381518e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/e8d58cc58141964336fae8d8952e30cd.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5352049476)*(0.369876310e-1-0.3638127575e-2*Ce)+(-.1337432288+.8970894976*Ce)*(0.1849381518e-1-0.1819063782e-2*Ce)-Ce*(0.1849381518e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/111e7175e19ac17553cb42474aec67cc.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_22` := (0.1455251030e-2*Ce+.5356096675)*(0.355258312e-1-0.3638127575e-2*Ce)+(.8*(-.1184158360+1.121361872*Ce))*(0.1776291535e-1-0.1819063782e-2*Ce)-Ce*(0.1776291535e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/fda5161784fa985e4c03b6001792a841.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5356096675)*(0.355258312e-1-0.3638127575e-2*Ce)+(-0.9473266880e-1+.8970894976*Ce)*(0.1776291535e-1-0.1819063782e-2*Ce)-Ce*(0.1776291535e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/859d1f57b125b1f2f441864466b72190.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_32` := (0.1455251030e-2*Ce+.5356038465)*(0.355403838e-1-0.3638127575e-2*Ce)+(.8*(-.1179012835+1.121361872*Ce))*(0.1777019161e-1-0.1819063782e-2*Ce)-Ce*(0.1777019161e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/f6b9afd44ddab16b192f3f82420397ed.gif" style="vertical-align:-24px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(0.1455251030e-2*Ce+.5356038465)*(0.355403838e-1-0.3638127575e-2*Ce)+(-0.9432102680e-1+.8970894976*Ce)*(0.1777019161e-1-0.1819063782e-2*Ce)-Ce*(0.1777019161e-1-0.1819063782e-2*Ce)" height="43" src="/view.aspx?sf=241972_question/e61df1afc69eed9033124f6f5e20a009.gif" style="vertical-align:-24px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S12 := plot(`&amp;amp;Pi;_12`, Ce = 0 .. 0.9e-1, color = [red], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer Profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;W&amp;quot;));`]); S22 := plot(`&amp;amp;Pi;_22`, Ce = 0 .. 0.9e-1, color = [green], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;D&amp;quot;));`]); S32 := plot(`&amp;amp;Pi;_32`, Ce = 0 .. 0.9e-1, color = [blue], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;S&amp;quot;));`])" height="106" src="/view.aspx?sf=241972_question/d63d30fa552b4284847f8def67ee3477.gif" style="vertical-align:-87px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/3b4bf557adf9fdb20c746a4387b6ffa1.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/a361c6f163856a09e6ff6f5993f94515.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/9f6a25a20f58af53743c9eccf56fa465.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_1` := (-0.60726413e-1*Ce+.6173851967)*(0.1849381518e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1849381518e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/867651a524b8d986d45dd59abef6fc8b.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.6173851967)*(0.1849381518e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1849381518e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/ca47d303080a1416682439c056736698.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_2` := (-0.60726413e-1*Ce+.5929853242)*(0.1776291535e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1776291535e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/20543c34700a6e0dc5b6e875f21ec38f.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.5929853242)*(0.1776291535e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1776291535e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/667cc56b27c1e32cc5229e3bfa24dccd.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="`&amp;amp;Pi;_3` := (-0.60726413e-1*Ce+.5932282299)*(0.1777019161e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1777019161e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/339fcff31edbf4f205e7257350a1597b.gif" style="vertical-align:-28px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="(-0.60726413e-1*Ce+.5932282299)*(0.1777019161e-1-0.1819063782e-2*Ce)-0.2500000000e-1*(0.1777019161e-1-0.1819063782e-2*Ce)^2" height="47" src="/view.aspx?sf=241972_question/868ff5001322e9db4611bc71a25712bc.gif" style="vertical-align:-28px" width="738"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="S1 := plot(`&amp;amp;Pi;_1`, Ce = 0 .. 0.9e-1, color = [yellow], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;W&amp;quot;));`]); S2 := plot(`&amp;amp;Pi;_2`, Ce = 0 .. 0.9e-1, color = [black], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer  profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`]); S3 := plot(`&amp;amp;Pi;_3`, Ce = 0 .. 0.9e-1, color = [grey], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;S&amp;quot;));`])" height="106" src="/view.aspx?sf=241972_question/9eca2e4620324f7ec9c0a00b040c6e15.gif" style="vertical-align:-87px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/5ab1ca265166b47f3a6c3c0553f24b6c.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/82f729995cd77c6e2faebd8cf2abd9d3.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/78d6747a3b0c0858e0d03aaff43694f8.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="dualaxisplot(plot(`&amp;amp;Pi;_22`, Ce = 0 .. 0.9e-1, color = [&amp;quot;red&amp;quot;], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Manufacturer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;m&amp;quot;),mn(&amp;quot;D&amp;quot;));`]), plot(`&amp;amp;Pi;_2`, Ce = 0 .. 0.9e-1, color = [&amp;quot;green&amp;quot;], labels = [&amp;quot;Ce&amp;quot;, &amp;quot;Retailer profit&amp;quot;], labeldirections = [&amp;quot;horizontal&amp;quot;, &amp;quot;vertical&amp;quot;], legend = [`#msubsup(mi(&amp;quot;Pi&amp;quot;),mi(&amp;quot;r&amp;quot;),mn(&amp;quot;D&amp;quot;));`]), title = &amp;quot;fairnes cost Comparison&amp;quot;)" height="86" src="/view.aspx?sf=241972_question/6d57b836614ebe9cb2531071793ba4c8.gif" style="vertical-align:-67px" width="768"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/3c1ee4cb8a0e17edc91d7da30d850a29.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="display({S1, S12, S2, S22, S3, S32})" height="23" src="/view.aspx?sf=241972_question/6bdb47227635e872f6826e4bdde67a72.gif" style="vertical-align:-6px" width="232"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" height="400" src="/view.aspx?sf=241972_question/18e040119b17e6033353ef105a544da3.gif" style="border:none" width="400"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=241972_question/05e23dd6819bc4b7b01ac683ba789d03.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=241972_question/All_plots_Combined.mw"&gt;Download All_plots_Combined.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>241972</guid>
      <pubDate>Sun, 09 Nov 2025 16:33:49 Z</pubDate>
      <itunes:author>Andiguys</itunes:author>
      <author>Andiguys</author>
    </item>
  </channel>
</rss>