Explanation Given information: The revenue from selling q items is R ( q ) = 450 q and the total cost is C ( q ) = 10 , 000 + 3 q 2 Formula used: The profit π ( q ) is the difference between the revenue, R ( q ) , and the cost, C ( q ) , of supplying that quantity. ⇒ π ( q ) = R ( q ) − C ( q ) Fact used: If f ' changes from negative to positive at p, then f has a local minimum at p. f ' changes from positive to negative at p, then f has a local maximum at p. Calculation: The profit is given by π ( q ) = R ( q ) − C ( q ) π ( q ) = 450 q − ( 10 , 000 + 3 q 2 ) = − 10 , 000 + 450 q − 3 q 2 ⇒ π ( q ) = − 10 , 000 + 450 q − 3 q 2 Differentiating with respect to ‘q’, we get π ' ( q ) = 450 − 6 q To find the quantity that maximizes the profit, equate π ' ( q ) = 0

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.4, Problem 3P

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To find:

Thequantity that maximizes the profit and the total profit at this production level.

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Chapter 4.4, Problem 2P

Chapter 4.4, Problem 4P

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P Ch. 4.1 - Prob. 13P Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - Prob. 16P Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 20P Ch. 4.1 - Prob. 21P Ch. 4.1 - Prob. 22P Ch. 4.1 - Prob. 23P Ch. 4.1 - Prob. 24P Ch. 4.1 - Prob. 25P Ch. 4.1 - Prob. 26P Ch. 4.1 - Prob. 27P Ch. 4.1 - Prob. 28P Ch. 4.1 - Prob. 29P Ch. 4.1 - Prob. 30P Ch. 4.1 - Prob. 31P Ch. 4.1 - Prob. 32P Ch. 4.1 - Prob. 33P Ch. 4.1 - Prob. 34P Ch. 4.1 - Prob. 35P Ch. 4.1 - Prob. 36P Ch. 4.1 - Prob. 37P Ch. 4.1 - Prob. 38P Ch. 4.1 - Prob. 39P Ch. 4.1 - Prob. 40P Ch. 4.1 - Prob. 41P Ch. 4.1 - Prob. 42P Ch. 4.1 - Prob. 43P Ch. 4.1 - Prob. 44P Ch. 4.1 - Prob. 45P Ch. 4.1 - Prob. 46P Ch. 4.1 - Prob. 47P Ch. 4.1 - Prob. 48P Ch. 4.1 - Prob. 49P Ch. 4.1 - Prob. 50P Ch. 4.1 - Prob. 51P Ch. 4.1 - Prob. 52P Ch. 4.1 - Prob. 53P Ch. 4.1 - Prob. 54P Ch. 4.1 - Prob. 55P Ch. 4.1 - Prob. 56P Ch. 4.1 - Prob. 57P Ch. 4.1 - Prob. 58P Ch. 4.2 - Prob. 1P Ch. 4.2 - Prob. 2P Ch. 4.2 - 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Thequantity that maximizes the profit and the total profit at this production level.

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To find: Thequantity that maximizes the profit and the total profit at this production level.

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Chapter 4 Solutions

To find:

Thequantity that maximizes the profit and the total profit at this production level.