A company manufactures commercial heating system components and domestic furnaces at its factories in Monaca, PA and Hamburg, NY. At the Monaca plant, no more than 1000 units per day can be produced, and the number of commercial components cannot exceed 100 more than half the number of domestic furnaces. At the Hamburg plant, no more than 850 units per day can be produced. The profit on each commercial component is $400 at the Monaca plant and $390 at the Hamburg plant. The profit on each domestic furnace is $200 at the Monaca plant and $215 at the Hamburg plant. If there is a rush order for 500 commercial components and 750 domestic furnaces, how many of each should be produced at each plant in order to maximize profits? Find the maximum profit. Note: Assume that exactly enough units are produced to fill the rush order.
A) Maximum profit is $344,500 with 200 heating comproments produced at Monaca and 300 at Hamburg and 550 domestic furnces produced at Monaca and 200 at Hamburg.
B) Maximum profit is $364,000 with 300 heating comproments produced at Monaca and 200 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.
C) Maximum profit is $355,250 with 200 heating comproments produced at Monaca and 300 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.
D) Maximum profit is $368,500 with 300 heating comproments produced at Monaca and 200 at Hamburg and 550 domestic furnces produced at Monaca and 200 at Hamburg.
E) Maximum profit is $365,750 with 200 heating comproments produced at Monaca and 300 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.

Question

A company manufactures commercial heating system components and domestic furnaces at its factories in Monaca, PA and Hamburg, NY. At the Monaca plant, no more than 1000 units per day can be produced, and the number of commercial components cannot exceed 100 more than half the number of domestic furnaces. At the Hamburg plant, no more than 850 units per day can be produced. The profit on each commercial component is $400 at the Monaca plant and $390 at the Hamburg plant. The profit on each domestic furnace is $200 at the Monaca plant and $215 at the Hamburg plant. If there is a rush order for 500 commercial components and 750 domestic furnaces, how many of each should be produced at each plant in order to maximize profits? Find the maximum profit. Note: Assume that exactly enough units are produced to fill the rush order. ​
A) Maximum profit is $344,500 with 200 heating comproments produced at Monaca and 300 at Hamburg and 550 domestic furnces produced at Monaca and 200 at Hamburg.
B) Maximum profit is $364,000 with 300 heating comproments produced at Monaca and 200 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.
C) Maximum profit is $355,250 with 200 heating comproments produced at Monaca and 300 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.
D) Maximum profit is $368,500 with 300 heating comproments produced at Monaca and 200 at Hamburg and 550 domestic furnces produced at Monaca and 200 at Hamburg.
E) Maximum profit is $365,750 with 200 heating comproments produced at Monaca and 300 at Hamburg and 200 domestic furnces produced at Monaca and 550 at Hamburg.

Quizplus · Accepted Answer

The maximum profit is achieved by producing 200 commercial components at Monaca and 300 at Hamburg, and 200 domestic furnaces at Monaca and 550 at Hamburg, resulting in a profit of $355,250.

A Company Manufactures Commercial Heating System Components and Domestic Furnaces