Calculus: Graphical, Numerical, Algebraic
Calculus: Graphical, Numerical, Algebraic
3rd Edition
ISBN: 9780133688399
Author: Finney, Ross L.
Publisher: Pearson/Prentice Hall
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Differential Equations
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Chapter 5.4, Problem 25E
To determine

Find the production level that minimizes average cost.

Expert Solution & Answer
Check Mark

Answer to Problem 25E

The production level x=5000 average cost is minimum.

Explanation of Solution

Given information: Given the cost is c(x)=x3−10x2−30x

Calculation:

The average cost is,

  cavg=c(x)x      =x3−10x2−30xx       =x2−10x−30

The average cost will be minimum or maximum at c′avg(x)=0 and the average cost will be minimum if c′avg"(x)>0

  cavg(x)=x2−10x−30c′avg(x)=02x−10=0x=5c′avg(x)=2x−10cavg"(x)=2>0

It shows that x=5 corresponds to minimum average cost. Since x is measured in thousands of units x=5000 .

Thus, the production level x=5000 average cost is minimum.

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Chapter 5.4, Problem 24E
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Chapter 5.4, Problem 26E

Chapter 5 Solutions

Calculus: Graphical, Numerical, Algebraic

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