# The marginal cost function if the cost function is C ( x ) = 2000 + 3 x + 0.01 x 2 + 0.0002 x 3 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.8, Problem 29E

(a)

To determine

## To find: The marginal cost function if the cost function is C(x)=2000+3x+0.01x2+0.0002x3.

Expert Solution

The marginal cost function is, C'(x)=3+0.02x+0.0006x2.

### Explanation of Solution

The cost function is C(x)=2000+3x+0.01x2+0.0002x3.

Obtain the derivative of the cost function and obtain the marginal function.

C'(x)=ddx(2000+3x+0.01x2+0.0002x3)=3+0.02x+0.0006x2

Thus, the marginal cost function is, C'(x)=3+0.02x+0.0006x2.

(b)

To determine

Expert Solution

(c)

To determine

Expert Solution

The cost of manufacturing the 101st pair of jeans is approximately $11.07. ### Explanation of Solution From part (b), the value of C'(100)=$11/pair.

The cost of manufacturing the 101st pair of jeans is calculated by, C(101)C(100).

Substitute x = 100 in C(x) and find the value of C(100).

C(100)=2000+3(100)+0.01(100)2+0.0002(100)3=2000+300+100+200=2600

Substitute x = 101 in C(x) and find the value of C(101).

C(101)=2000+3(101)+0.01(101)2+0.0002(101)3=2000+303+102.01+206.0602=2611.0702

Substitute the respective values in C(101)C(100),

C(101)C(100)=2611.07022600=11.0702

The cost of manufacturing the 101st pair of jeans is approximately \$11.07, which is very close to the marginal cost of C'(100).

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