Chapter 5, Problem 84RE

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Profit The marginal profit obtained by selling x dollars of automobile insurance can be modeled by d p d x = 0.4 ( 1 − 5000 x ) ,   x ≥ 5000 .Find the change in the profit P (in dollars) when x increases from $75,000 to$100,000.

To determine

To calculate: The change in profit when x increases from $75,000 to$100,000 dollars, if the

marginal profit is modeled by dPdx=0.4(15000x),x5000.

Explanation

Given information:

The marginal profit is modeled by dPdx=0.4(15000x),x5000 where x is the selling amount

in dollars.

Formula used:

Marginal analysis:

x1x2dRdxdx=R(x2)R(x1)

Calculation:

Consider the function is dPdx=0.4(15000x).

Use Marginal analysis where x2=100000 and x1=75000

75000100000(0.42000x)dx=[0.4x2000ln|x|]75000100000                            =[0

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