   Chapter 4.5, Problem 78E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Minimum Average Cost The cost of producing x units of a product is modeled by C =   100   +   25 x −   120   ln x , x ≥   1 .(a) Find the average cost function C.(b) Find the minimum average cost analytically. Use a graphing utility to confirm your result.

(a)

To determine

To calculate: The average cost function C¯ if the model of cost for producing x of an item is C=100+25x120lnx,  x1

Explanation

Given Information:

The model of cost for producing x of an item is C=100+25x120lnx,  x1

Formula used:

If the cost of producing x number of items is C then the average cost of the function is basically the total cost divided by total number of items produced given by.

C¯=Cx

Calculation:

Consider the model, C=100+25x120lnx

Evaluate the average cost by dividing the cost function by number of items.

Here, number of items produced are x

(b)

To determine

To calculate: The minimum average cost if the model of cost for producing x of an item is C=100+25x120lnx,  x1, also verify the result using graphing utility.

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