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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
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 + 500 x 1.6 x 2 + 0.004 x 3 is the cost function and p ( x ) = 1700 7 x is the demand function, find the production level that will maximize profit.

To determine

a)

To show:

If the profit P(x) is Maximum, then the marginal revenue equals the marginal cost

Explanation

1) Concept:

In order to maximize profit, we need to find critical numbers of P

A critical number of a function f   is a number c in the domain of f  Such that either  f'c=0 or f'c does not exist.

2) Given:

The profit P(x) is Maximum

3) Calculation:

The total profit is Px=Rx-C(x)

To maximize profit differentiate Px

P'

To determine

b)

To find:

The production level that will maximize profit

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