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Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
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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