Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.4P
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Only solve part D.
![3. The total cost for a company to produce x units of a certain commodity is given by
C(x) = 4x2 + 83x + 144.
Market research finds that if the company produces x units of the product, the
maximum price per unit that they should charge in order to sell all of them is given
by
p(x) = 237 – 3x.
(a) Use marginal analysis to estimate the cost of producing the eighth unit.
(b) Find the actual cost of producing the eighth unit.
(c) Find the level of production that maximizes the company's profits, and calculate
the maximum profit.
(d) Find the minimum average production cost per unit and the level of production
that minimizes this average cost.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07c18519-6114-4913-a423-a4b4e83c124c%2Fcd50b1a6-cf6a-4f2b-9f5e-ad268fc7dd8f%2F4h4vr7xa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. The total cost for a company to produce x units of a certain commodity is given by
C(x) = 4x2 + 83x + 144.
Market research finds that if the company produces x units of the product, the
maximum price per unit that they should charge in order to sell all of them is given
by
p(x) = 237 – 3x.
(a) Use marginal analysis to estimate the cost of producing the eighth unit.
(b) Find the actual cost of producing the eighth unit.
(c) Find the level of production that maximizes the company's profits, and calculate
the maximum profit.
(d) Find the minimum average production cost per unit and the level of production
that minimizes this average cost.
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