Chapter 13.3, Problem 36E

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# Sales and advertising The figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $4 million is used in advertising rather than$2 million.

To determine

To calculate: The integral that represents the extra sales growth if $4 million is used in advertising rather than$2 million where the sales growth rate under different levels of distribution and advertising from a to b are shown.

Explanation

Given information:

The sales growth rate under different levels of distribution and advertising from a to b are shown as:

Formula used:

Area between two Curves:

If f and g are continuous functions on [a,b] and if f(x)g(x) for all x in [a,b] then the area of the region between the graphs of f and g are given and between x=a and x=b is given by:

A=ab[f(x)g(x)dx]

Calculation:

Consider the figure:

The $4 Million advertising is represented by the function f and the$2 Million advertising is represented by the function h.

As the extra sales growth is to be determined if the $4 Million adverting is used instead of$2 Million and it is given by the area between the curve of f and h

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