Explanation Given Information: Total cost function C ( x ) = 900 + 25 x Total revenue function R ( x ) = 100 x − x 2 Formula Used: The vertex point is x = − b 2 a where b is the coefficient of x and a is the coefficient of x 2 . The formula of the profit function is, P ( x ) = R ( x ) − C ( x ) , The general profit function P ( x ) = a x 2 + b x + c . Calculation: To find the maximum revenue, first find the vertex point. From the revenue function, a = − 1 and b = 100 . Substitute 100 for b and − 1 for a in the formula of vertex point. x = − b 2 × a = − 100 2 × ( − 1 ) = 100 2 = 50 To find the maximum value of the revenue function, substitute 50 for x in the revenue function. R ( 50 ) = 100 ( 50 ) − ( 50 ) 2 = 5000 − 2500 = 2500 Thus, the maximum value of the revenue function is 2500

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

12th Edition

ISBN: 9781337630542

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 2, Problem 59RE

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To calculate: The maximum revenue and maximum profit for the cost function C(x)=900+25x and the revenue function R(x)=100x−x2.

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Chapter 2, Problem 58RE

Chapter 2, Problem 60RE

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WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

Ch. 2.1 - The factoring method for solving a quadratic...Ch. 2.1 - Solve the following equations by factoring. Ch. 2.1 - Prob. 3CP Ch. 2.1 - Prob. 4CP Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 6E

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The maximum revenue and maximum profit for the cost function C ( x ) = 900 + 25 x and the revenue function R ( x ) = 100 x − x 2 .

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To calculate: The maximum revenue and maximum profit for the cost function C(x)=900+25x and the revenue function R(x)=100x−x2.

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