   Chapter 13.5, Problem 39E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# Cost Suppose that the marginal cost for x units of a good is M C ¯ = x 2 + 9 (dollars per unit) and the fixed cost is $300.(a) What is the total cost function of the good?(b) What is the total cost of producing 4 units of this good? (a) To determine To calculate: The total cost function of the good if marginal cost for x units of a good is MC¯=x2+9 and the fixed cost is$300.

Explanation

Given Information:

Marginal cost for x units of a good is,

MC¯=x2+9

And the fixed cost is $300. Formula used: Marginal cost for x units of a good is, MC¯=x2+9 The integral formula, u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C Calculation: As it is provided that marginal cost for x units of a good is, MC¯=x2+9 Now, to obtain the total cost function, integrate the marginal cost function as the marginal cost function is the derivative of total cost function, so, C(x)=x2+9dx Now, use formula 6 of table to evaluate the integral as, C(x)=x2+9dx (b) To determine To calculate: The total cost of producing 4 units of good if marginal cost for x units of a good is MC¯=x2+9 and the fixed cost is$300.

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