Explanation Given information: To produce 1000 items, the total cost is $5000 and the marginal cost is $25 per item. Concept Used: To produce q items, the total cost is C ( q ) , then the marginal cost is C ′ ( q ) per item. The marginal cost of q items can be written as C ′ ( q ) = C ( q + n ) − C ( q ) q + n − q Calculation: From the given information, C ' ( 1000 ) = 25 , C ( 1000 ) = 5000 . We can write the marginal cost for 1000 item as follows, C ' ( 1000 ) = C ( 1001 ) − C ( 1000 ) 1001 − 1000 Substituting the given constants as follows, 25 = C ( 1001 ) − 5000 1 25 = C ( 1001 ) − 5000 C ( 1001 ) = 25 + 5000 = $ 5025 We can write the marginal cost for 999 item as follows

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 2.5, Problem 12P

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To estimate:

The costs of producing 1001 items, 999 items, and 1100 items.

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Chapter 2.5, Problem 11P

Chapter 2.5, Problem 13P

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Chapter 2 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To estimate: The costs of producing 1001 items, 999 items, and 1100 items.

Solution Summary: The author estimates the costs of producing 1001 items, 999 items and 1100 items.