Suppose that for a certain product the marginal cost is determined by means of C ^ '(x) = 1.02 (x + 200) ^ (0.02) and the marginal revenue by means of I ^' (x) = 2 / √ (4x + 1) +1.75, where x is in unit miles and income and cost are in dollar miles. Suppose further that fixed costs are 150 thousand dollars and that production is limited to a maximum of 200 thousand units. a) Find C (x) and I (x). b) Determine the level of

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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Suppose that for a certain product the marginal cost is determined by means of C ^ '(x) = 1.02 (x + 200) ^ (0.02) and the marginal revenue by means of I ^' (x) = 2 / √ (4x + 1) +1.75, where x is in unit miles and income and cost are in dollar miles. Suppose further that fixed costs are 150 thousand dollars and that production is limited to a maximum of 200 thousand units.

a) Find C (x) and I (x).

b) Determine the level of production that gives maximum profit and find the maximum profit (or loss).

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