Chapter 12.4, Problem 4E

### 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

# TOTAL COST AND PROFITIn Problems 1-12, cost, revenue, and profit are in dollars and x is the number of units.If the marginal cost for a product is M C ¯ = 3 x +   50 and the total cost of producing 20 units is $2000, find the total cost function. To determine To calculate: The total cost function if the marginal cost for a product is MC¯=3x+50 and the production of 20 units results in total cost of$2000.

Explanation

Given information:

It is provided that the marginal cost for a product is MC¯=3x+50 and the production of 20 units results in total cost of \$2000.

Formula used:

Total Cost:

C(x)=MC¯dx

Where MC¯ is defined as the marginal cost.

The integral formula,

xndx=xn+1n+1+K

Where K is a constant.

Calculation:

Consider the marginal cost:

MC¯=3x+50

Consider the formula:

C(x)=MC¯dx

Substitute 3x+50 for MC¯ in above equation to get:

C(x)=(3x+50)dx

Solve by the use of integral formula, xndx=x

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