Question: A company operates two plants which manufacture the same item and whose total cost functions are C 1 = 8.5 + 0.03q 2 1 and

A company operates two plants which manufacture the same item and whose total cost functions are

C₁ = 8.5 + 0.03q²₁ and C₂ = 5.2 + 0.04q²₂,

where q₁ and q₂ are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q = q₁ + q₂, is related to the price, p, by

p = 60 − 0.04q.

How much should each plant produce in order to maximize the company’s profit?

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