Explanation Given: The marginal profit of a small car agency is computed as P ′ ( x ) = x 2 + 3 x where the profit P ( x ) is in dollars. Integration Formula used: Rational function: ∫ u a + b u d u = 2 ( 3 b u − 2 a ) 15 b 2 ( a + b u ) 3 Calculation: Integrate the marginal profit and obtain the profit P ( x ) as follows. P ( x ) = ∫ P ′ ( x ) d x = ∫ x 2 + 3 x d x = 2 ( 3 ( 3 ) x − 2 ( 2 ) ) 15 ( 3 ) 2 ( 2 + 3 x ) 3 + C ; a = 2 , b = 3 and u = x = 2 ( 9 x − 4 ) 15 × 9 ( 2 + 3 x ) 3 + C On further computation, P ( x ) = 2 ( 9 x − 4 ) 15 × 9 ( 2 + 3 x ) 3 + C = 18 x − 8 135 ( 2 + 3 x ) 3 + C As the weekly profit on 1 car is -$2,000, compute the equation P ( 1 ) = − 2000 as follows

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 6.4, Problem 85E

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To find: The profit function and the number of cars that must be sold that generates a profit of $13,000 per week. Also find the weekly profit that the agency will have on the sale of 80 cars per week.

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Chapter 6.4, Problem 84E

Chapter 6.4, Problem 86E

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Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

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The profit function and the number of cars that must be sold that generates a profit of $13,000 per week. Also find the weekly profit that the agency will have on the sale of 80 cars per week.

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To find: The profit function and the number of cars that must be sold that generates a profit of $13,000 per week. Also find the weekly profit that the agency will have on the sale of 80 cars per week.

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Chapter 6 Solutions