   Chapter 12.1, Problem 49E ### 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

# Average cost The DeWitt Company has found that the rate of change of its average cost for a product is C ' ¯ ( x ) = 1 4 − 100 x 2 where x is the number of units and cost is in dollars. The average cost per unit for 20 units is $400.(a) Find the average cost function for the product.(b) Find the average cost of 100 units of the product. (a) To determine To calculate: The average cost function if rate of change of average cost for a product is C¯(x)=14100x2. Explanation Given Information: The rate of change of average cost for a product is, C¯(x)=14100x2 Where x is the number of units and cost is in dollars. Also, the average cost for 20 units is$400.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

As it is provided that the rate of change of average cost for a product is,

C¯(x)=14100x2

Where x is the number of units and cost is in dollars.

Now, to obtain the average cost function, C¯(t), integrate the above equation with respect to x as,

C¯(x)dx=(14100x2)dx

Use the power rule o

(b)

To determine

To calculate: The average cost of 100 units of the product if rate of change of average cost for a product is C¯(x)=14100x2.

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