To account for a higher demand of office chairs, a manufacturer has decided to o

Question

To account for a higher demand of office chairs, a manufacturer has decided to open 2 new plants to handle the demand. Plant A will have fixed costs of $8,300 per month, and variable costs of $47.50 per chair. The maximum production of Plant A is 500 chairs per month. Plant B will have a fixed cost of $10,000 per month, and variable costs of $45.00 per chair. The maximum production of Plant B is also 500 chairs. Suppose that the office chairs sell for $100 each. What volume per month will ensure that Plant A breaks even? What volume per month will ensure that Plant B breaks even? What volume is needed to obtain a profit of $10,000 in each of the plants? Assuming that you are required to run one plant to maximum capacity, which plant would you choose? Explain.

Explanation / Answer

say number of chairs = x

PLANT A:

cost=8300+47.50x

x<=500

revenue=100x

Profit=Revenue-cost=100x-(8300+47.50x)=52.5x-8300

at break even, we know that cost=revenue so we get

8300+47.50x=100x

8300=52.5x

8300/52.5=x

x=158.095238095

so approx 158 chairs are needed to break even.

-------------

Given that Profit=10000

then 52.5x-8300=10000

52.5x=18300

x=348.571428571

so we need approx 349 chairs to get profit of $10000.

---------------

PLANT B:

cost=10000+45x

x<=500

revenue=100x

at break even, we know that cost=revenue so we get

10000+45x=100x

10000=55x

10000/55=x

x=181.818181818

so approx 182 chairs are needed to break even.

---------------

Profit=Revenue-cost=100x-(10000+45x)=55x-10000

Given that Profit=10000

then 55x-10000=10000

55x=20000

x=363.636363636

so we need approx 364 chairs to get profit of $10000.

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