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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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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