   Chapter 11.1, Problem 43E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Marginal cost Suppose that the total cost (in dollars) for a product is given by where x is the number of units produced. C ( x ) = 1500 + 200  In ( 2 x + 1 ) (a) Find the marginal cost function.(b) Find the marginal cost when 200 units are produced and interpret your result.(c) Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function? Does it apply in this problem?

(a)

To determine

To calculate: The marginal cost function of the total cost C(x)=1500+200ln(2x+1).

Explanation

Given Information:

The total cost (in dollars) for a product is given by,

C(x)=1500+200ln(2x+1)

Where x denotes the number of units produced.

Formula Used:

The derivative property of logarithm,

ddx(lnx)=1x

The derivative of chain rule,

ddxf(g(x))=fg(x)g(x)

Calculation:

Consider the provided function C(x)=1500+200ln(2x+1).

Differentiate the provided cost function,

ddx(C(x))=ddx(1500+200ln(2x+1))=ddx(1500)+ddx(200ln(2x+1))

Use the chain rule to get,

MarginalCost(C(x))=ddx(1500+200ln(2x+1)

(b)

To determine

To calculate: The marginal cost when 200 units are produced and interpret the result.

(c)

To determine

The condition which must be true for the marginal cost function. Also determine if the condition apply on the given problem or not.

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