Suppose a company owns two plants, plant A and plant B. The total cost functions

Question

Suppose a company owns two plants, plant A and plant B. The total cost functions are as follows:

Plant A: TCA = 5qA + 0.1qA2

Plant B: TCB = 5qB + 0.2qB2

1. Suppose that the company is a price taker and the market price is $10. How many units will each plant produce?

2. Suppose that the company decides to produce 100 units of its product in total. how many units will be produced in each plant? what will be the total cost of the 100 units?

Explanation / Answer

1. The company is looking to maximize profit from both plants; the Profit function for Plant A would be 10qA - (5qA + 0.1qA^2) and Plant B would be 10qB - (5qB + 0.2qB^2). Plant A maximum profit quantity = 25 ($62.50) Plant B maximum profit quantity = 12.5 --> 12 or 13 would give the same profit ($31.20) 2. The company wants to minimize total cost/maximize profit 100 of Plant A would cost $1,500 100 of Plant B would cost $2,500 There is no combination of A and B that would beat purely producing from Plant A; the company would produce 100 units from plant A. Hope this helps!

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