(a) Explanation Given: The annual savings in dollars per year at the rate of: S ′ ( x ) = 150 − x 2 Where, x is the number of years of operation. And the annual costs in dollars per year at the rate of: C ′ ( x ) = x 2 + 11 4 x Calculation: The maximum savings will occur when the rate of savings equals the rate of cost. Then, for maximum savings: S ′ ( x ) = C ′ ( x ) 150 − x 2 = x 2 + 11 4 x 2 x 2 + 11 4 x − 150 = 0 8 x 2 + 11 x − 600 = 0 (b) To determine To calculate: The net savings during the first year of the use of the new machine. (c) To determine To calculate: The net savings during the use of the new machine for 8 years.

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 13.5, Problem 23E

(a)

To determine

To calculate: The number of years to maximize the net savings.

(b)

To determine

To calculate: The net savings during the first year of the use of the new machine.

(c)

To determine

To calculate: The net savings during the use of the new machine for 8 years.

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Chapter 13.5, Problem 22E

Chapter 13.5, Problem 24E

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Chapter 13 Solutions

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - Prob. 9CP Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...

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