   Chapter 4.7, Problem 60E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost.(b) If C(x) = 16,000 + 500x − 1.6x2 + 0.004x3 is the cost function and p(x) = 1700 − 7x is the demand function, find the production level that will maximize profit.

(a)

To determine

To show: The marginal revenue is equal to the marginal cost if profit P(x) is a maximum.

Explanation

Given:

The profit P(x) is a maximum.

Calculation:

The total profit is P(x)=R(x)C(x)

Where R(x)= selling cost.

C(x)= Production cost

Differentiate P with respect to x

dPdx=dRdxdCdx

For critical points, dPdx=0

(b)

To determine

To find: The production level that will maximize profit

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