A television manufacturer 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 let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.

b. The manufacturer is bound by the following constraints:
• Equipment in the factory allows for making at most 450 rear-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 unit is $600 for the rear-projection televisions 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 be nonnegative.
d. Evaluate the objective function for 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 manufacturer will make the greatest profit by manufacturing__________ rear-projection televisions each month and_________ plasma televisions each month. The maximum monthly profit is $____________ .