a. Explanation Given: The cost function is C ( x ) = − 0.02 x 2 + 400 x + 5000 . Definition: (1) Average cost : “The cost function C ( x ) gives the cost to produce the first x items in a manufacturing process. The average cost to produce x items is C ¯ ( x ) = C ( x ) x .” (2) Marginal cost : “The marginal cost C ′ ( x ) is the approximate cost to produce one additional item after producing x items.” Calculation: The average cost function for x = 3000 is computed as follows, C ¯ ( 3000 ) = C ( 3000 ) 3000 = − 0.02 ( 3000 ) 2 + 400 ( 3000 ) + 5000 3000 = 1025000 3000 ≈ 341.67 Therefore, the average cost function for x = 3000 is C ¯ ( 3000 ) ≈ $ 341 b. To determine To interpret: The values obtained in part (a).

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Question

Chapter 3, Problem 65RE

To determine

The average cost and marginal cost for x=3000 lawnmowers.

To determine

To interpret: The values obtained in part (a).

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Chapter 3, Problem 64RE

Chapter 3, Problem 66RE

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