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 ?? = the number of rear-projection televisions manufactured in a month and ?? = 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
? 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 profit is $______.
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