http://www.mapleprimes.com/questions/140581-Minimize-Of-Sides-In-A-Volume en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 21:24:50 GMT Wed, 10 Jun 2026 21:24:50 GMT The latest answers and comments added to the Question, Minimize of sides in a volume http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/140581-Minimize-Of-Sides-In-A-Volume http://www.mapleprimes.com/questions/140581-Minimize-Of-Sides-In-A-Volume?ref=Feed:MaplePrimes:Minimize of sides in a volume:Comments#answer140608 <p>Express&nbsp; &nbsp;<strong>z</strong>&nbsp; &nbsp;through <strong>&nbsp;x</strong>&nbsp; and <strong>&nbsp;y</strong> , substitute into the formula for <strong>&nbsp;L</strong>&nbsp; and then find the minimum of the resulting function of two variables:</p> <p><strong>minimize(4*x+2*y+64/x/y, x&gt;0, y&gt;0, location);</strong></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 24, {[{x = 2, y = 4}, 24]}</p> <p>Express&nbsp; &nbsp;<strong>z</strong>&nbsp; &nbsp;through <strong>&nbsp;x</strong>&nbsp; and <strong>&nbsp;y</strong> , substitute into the formula for <strong>&nbsp;L</strong>&nbsp; and then find the minimum of the resulting function of two variables:</p> <p><strong>minimize(4*x+2*y+64/x/y, x&gt;0, y&gt;0, location);</strong></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 24, {[{x = 2, y = 4}, 24]}</p> 140608 Tue, 20 Nov 2012 21:25:47 Z Kitonum Kitonum http://www.mapleprimes.com/questions/140581-Minimize-Of-Sides-In-A-Volume?ref=Feed:MaplePrimes:Minimize of sides in a volume:Comments#answer140647 <p>A usual method for solving this sort of problem is to use Lagrange multipliers. That avoids having to solve the constraint for one of variables. Maple provides a routine for this,</p> <pre>(**) V := x*y*z:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<br>(**) L:=4*x+2*y+2*z:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<br>(**) Student[MultivariateCalculus][LagrangeMultipliers](L,[V-32],[x,y,z]);<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2<br>[2, 4, 4], [-1 + 3&nbsp;&nbsp;&nbsp; I, -2 + 2 I 3&nbsp;&nbsp; , -2 + 2 I 3&nbsp;&nbsp; ],<br><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2<br>&nbsp;&nbsp;&nbsp; [-1 - 3&nbsp;&nbsp;&nbsp; I, -2 - 2 I 3&nbsp;&nbsp; , -2 - 2 I 3&nbsp;&nbsp; ]<br><br></pre> <p>A usual method for solving this sort of problem is to use Lagrange multipliers. That avoids having to solve the constraint for one of variables. Maple provides a routine for this,</p> <pre>(**) V := x*y*z:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<br>(**) L:=4*x+2*y+2*z:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<br>(**) Student[MultivariateCalculus][LagrangeMultipliers](L,[V-32],[x,y,z]);<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2<br>[2, 4, 4], [-1 + 3&nbsp;&nbsp;&nbsp; I, -2 + 2 I 3&nbsp;&nbsp; , -2 + 2 I 3&nbsp;&nbsp; ],<br><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1/2<br>&nbsp;&nbsp;&nbsp; [-1 - 3&nbsp;&nbsp;&nbsp; I, -2 - 2 I 3&nbsp;&nbsp; , -2 - 2 I 3&nbsp;&nbsp; ]<br><br></pre> 140647 Wed, 21 Nov 2012 10:44:02 Z Joe Riel Joe Riel