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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 $$$
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Chapter 7 Solutions
Precalculus (6th Edition)
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