(a) To determine To calculate: The function for the cost if Rate of change in cost in thousands of dollars per year of a new production line is C ' ( x ) = 60 x 5 x 2 + 1 where x is the number of years and fixed cost is $ 10 thousand . Explanation Given: Rate of change in cost in thousands of dollars per year of a new production line is C ' ( x ) = 60 x 5 x 2 + 1 where x is the number of years and fixed cost is $ 10 thousand . Calculation: Consider the provided function and solve it: C ' ( x ) = 60 x 5 x 2 + 1 d C d x = 60 x 5 x 2 + 1 d C = 60 x 5 x 2 + 1 d x C = ∫ 60 x 5 x 2 + 1 d x Substitute ( 5 x 2 + 1 ) with t (b) To determine To calculate: Whether company should add new line after 5 years if New production line will be added if total cost of line for first 5 years remains below $ 40 , 000 . The total cost function is C = 6 ⋅ ln ( 5 x 2 + 1 ) + 10

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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Question

Chapter 13.2, Problem 41E

(a)

To determine

To calculate: The function for the cost if Rate of change in cost in thousands of dollars per year of a new production line is

C'(x)=60x5x2+1

where x is the number of years and fixed cost is $10 thousand.

(b)

To determine

To calculate: Whether company should add new line after 5 years if New production line will be added if total cost of line for first 5 years remains below $40,000.

The total cost function is

C=6⋅ln(5x2+1)+10

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Chapter 13.2, Problem 40E

Chapter 13.2, Problem 42E

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The function for the cost if Rate of change in cost in thousands of dollars per year of a new production line is C ' ( x ) = 60 x 5 x 2 + 1 where x is the number of years and fixed cost is $ 10 thousand .