A television manufacturer makes rear-projection andplasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.
a. Lei.
b. The manufacturer is bound by the following constraints:
• Equipment in the factory allows for making at most450 rear-projection televisions in one month.
• Equipment in the factory allows for making at most200 plasma televisions in one month.
• The cost to the manufacturer per unit is $600 for therear-projection televisions and $9DC for the plasmatelevisions. Total monthly costs cannot exceed$360,000.
Write a system of three inequalities that describes theseconstraints.
c. Graph the system of inequalities in pan (b). Use only the first quadrant and its boundary, because x and vmust both he nonnegative. 1
d. Evaluate the objective function for total monthly profitat each of the five vertices of the graphed region. [Thevertices should occur at (0,0), (0,200). (300,200),(450,100), and (450.0).] *
e. Complete the missing portions of this statement: Thetelevision manufacturer will make the greatest profit by
manufacturing 300 rear projection televisions
each month and
month. The maximum monthly profit is $77,500
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Thinking Mathematically (7th Edition)
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