Chapter 12, Problem 19T

### 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

# Suppose that the marginal cost for x units of a product is M C ¯ = 4 x + 50 , the marginal revenue is M R ¯ = 500 , and the cost of the production and sale of 10 units is $1000. What is the profit function for this product? To determine To calculate: The profit function where the marginal cost of production is MC¯=4x+50 and MR¯=500, and the total cost of production of 10 units is$1,000.

Explanation

Given information:

It is provided that the marginal cost of production is MC¯=4x+50 and MR¯=500 and the total cost of production of 10 units is \$1,000.

Formula used:

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.

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¯=4x+50 and MR¯=500

Consider the formula of revenue function,

R(x)=MR¯dx

Substitute 500 for MR¯ in above equation to get,

R(x)=(500)dx=500x

Consider the formula of cost function,

C(x)=MC¯</

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