Explanation Given information: The revenue from selling q items is R ( q ) = 500 q − q 2 and the total cost is C ( q ) = 150 + 10 q 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 ) = 500 q − q 2 − ( 150 + 10 q ) = 500 q − q 2 − 150 − 10 q = − 500 +

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.4, Problem 2P

To determine

To write:

A function that gives the total profit earned and to find the quantity that maximizes the profit.

Expert Solution & Answer

Chapter 4 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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

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A function that gives the total profit earned and to find the quantity that maximizes the profit.

Solution Summary: The author explains the function that gives the total profit earned and to find the quantity that maximizes the profit.

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To write: A function that gives the total profit earned and to find the quantity that maximizes the profit.

Chapter 4 Solutions

To write:

A function that gives the total profit earned and to find the quantity that maximizes the profit.