   Chapter 2.7, Problem 29E

Chapter
Section
Textbook Problem

# Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C ( x ) = 2000 + 3 x + 0.01 x 2 + 0.0002 x 3 (a) Find the marginal cost function.(b) Find C′ (100) and explain its meaning. What does it predict?(c) Compare C′(100) with the cost of manufacturing the 101st pair of jeans.

To determine

Part (a)

To find: the marginal cost function.

Explanation

To find the marginal cost function, take derivative of given cost function.

1) Formula:

Power rule, ddxxn=n*xn-1

2) Given:

Cx=2000+3x+0.01x2+0.0002x3

3) Calculation:

C'x=ddx(2000+3x+0.01x2+0

To determine

Part (b)

To find: C'(100) and its meaning.

To determine

Part (c)

To compare: C'(x) with the cost of manufacturing the 101st pair of jeans.

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