Chapter 12, Problem 42RE

Mathematical Applications for the ...

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

Chapter
Section

Mathematical Applications for the ...

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

Profit Suppose a product has a daily marginal revenue M R ¯ =   46 and a daily marginal cost M C ¯ =   30   +   1 5 x , both in dollars per unit. If the daily fixed cost is $200, how many units will give maximum profit and what is the maximum profit? To determine To calculate: The optimal level of production where a firm has marginal cost of production is MC¯=30+15x and MR¯=46 and the daily fixed cost is$200.

Explanation

Given information:

It is provided that a firm has marginal cost of production is MC¯=30+15x, MR¯=46 and daily fixed cost is \$200.

Formula used:

The Optimal Production,

When marginal revenue equals to the marginal cost then the optimal production occurs.

MR¯=MC¯

The Total Cost,

C(x)=MC¯dx

Where MC¯ is defined as the marginal cost.

Total Revenue,

R(x)=MR¯dx

Where MR¯ is defined as the marginal cost.

The Profit,

The profit function P(x) is defined as the revenue function R(x) minus the cost function C(x)

P(x)=R(x)C(x)

Calculation:

Consider the marginal cost and marginal revenue:

MC¯=30+15x and MR¯=46

Use the formula of optimal profit,

30+15x=46

Solve to get,

15x=16x=80

Thus, maximum occurs at 80 units

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