Problem 1

A furniture manufacturer knows from experience that the cost of payroll and maintenance to run your shop s hours is a function of number of hours, s. The shape of the cost function in dollars and time in hours, C (s), determined by the manufacturer is:

C (s) = piecewise (s <16 and 0 <s,-s 3 +24 * ** ** 2 +20,16 s <= s, s * 20 +1748);

a) Define a function arrow that represents the cost of the manufacturer as a function of the operating hours in the workshop and plot this function in the range 0 to 40 hours:

b) With the function defined in (a) determines how many hours should operate the shop to make it a cost of $ 2,148 pesos:

c) Indicates in a graph similar to that performed in (a) point representing the time and cost considered in (b):

Problem 2

Consider the following system of two equations with two unknowns:

x ** 2 + y 2 = 4 **

y = (x-3/2) ** 2 +1

a) plotted on the xy plane the locus of points that satisfy the equations. Consider the values of two variables, x, y, between -3 and 3

b) Determine the coordinates (x, y) of the two points that satisfy both equations