A company’s market research department recommends the manufacture and marketing

Question

A company’s market research department recommends the manufacture and marketing of a new headphone set for iPhone X. After suitable test marketing, the research department presents the following demand function.

p = 66 - 2q

The financial department provides the cost function below.

C(q) = 82 + 18q   

where $82 is the estimate of fixed costs (tooling and overhead) and $18 is the estimate of marginal costs per headphone set (materials, labor, marketing, transportation, storage, etc.).

Find the maximum profit. (Round your answer to 2 decimal places, if necessary)

Explanation / Answer

the profit is maximum where the marginal cost is equal to marginal revenue

marginal cost =18

marginal revenue = increase in revenue with each increase in the quantity unit

formula , if p = a-bq then MR = a-2bq

p=66-2q then mr = 66-2*2q =>66-4q

by putting MR=MC
66-4q = 18
48 = 4q
q = 12

at quantity 12 , p = 66 - 2*12 = 42

revenue = q*p = 12*42 = 504
c= 82+ 18*12
=298
maximum profit = revenue - cost
=504-298
=206

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