Chapter 12.4, Problem 5E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In 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 MC ¯ = 140 + 0.15 and the total cost of producing 100 units is $25,000, find the total cost function and fixed costs. To determine To calculate: The total cost function and fixed costs if the marginal cost for a product is MC¯=140+0.15x and the total cost of producing 100 units is$25,000.

Explanation

Given information:

The marginal cost for a product is MC¯=140+0.15x and the total cost of producing 100 units is \$25,000.

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¯=140+0.15x

Consider the formula:

C(x)=MC¯dx

Substitute 140+0.15x for MC¯ in equation C(x)=MC¯dx and evaluate,

C(x)=(140+0.15x)dx=(140+0.15x1/2)dx

Use the integral formula xndx=xn+1n+1+K and evaluate further,

C(x)=140x+20.15x3/23+K=140x+

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