Chapter 4.5, Problem 15ES

A television manufacture makes rear – projection and plasma televisions. The profit per unit is $ 125 for the rear–projection televisions and $ 200 for the plasma televisions.

a. Let x = the number of rear – projection televisions manufactured in a month and y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.

The manufacture is bound by the following constraints:

Equipment in the factory allows for making at most 450 rears – projection televisions in one month.

Equipment in the factory allows for making at most 200 plasma televisions in one month.

The cost to the manufacturer per units is $600 for the rear–projection and $900 for the plasma televisions. Total monthly costs cannot exceed $360,000,

Write a system of three inequalities that models these constraints.

c. Graph the system of inequalities in part (b). Use only the first quadrant and its boundary

because x and y must both nonnegative

d. Evolutes the objective function for the total monthly profit at each of the five vertices of the graphed region. [The vertices should occur at (0.0), (0.200), (300,200), (450, 100), and (450.0).]

e. Complete the missing portions of this statement: The television manufacture will make the greatest profit by manufacturing ______ rear–projection television each month and _____ plasma television each month. The maximum monthly profit is $ __________.