Chapter 8.4, Problem 2E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# A company estimates that the marginal revenue (in dollars per unit) realized by selling x units of a product is 48 − 0.0012x. Assuming the estimate is accurate, find the increase in revenue if sales increase from 5000 units to 10,000 units.

To determine

To calculate: The increase in revenue if sales increase from 5,000 units to 10,000 units.

Explanation

Given information:

The marginal revenue by selling x units of product is 48âˆ’0.0012x.

The number of units varies from a=5,000â€‰units and b=10,000â€‰units.

Calculation:

Apply Net change Theorem as follows:

The integral of a rate of change is the net change

âˆ«abFâ€²(x)dx=F(b)âˆ’F(a) (1)

Here, the lower limit is a and the upper limit is b.

Apply Net Change Theorem to calculate the increase in revenue if sales increase from 5,000 units to 10,000 units.

Modify Equation (1) for calculation of revenue.

âˆ«abRâ€²(x)dx=R(b)âˆ’R(a) (2)

Substitute 5,000 units for a, 10,000 units for b, and 48âˆ’0.0012x for Râ€²(x) in Equation (2).

âˆ«5,00010,000(48âˆ’0

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