   Chapter 13.3, Problem 38E ### 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

# Inventory management The figure shows how an inventory of a product is depleted each quarter of a given year. What is the average inventory per month for the first 3 months for this product? [Assume that the graph is a line joining ( 0, 1300 )  and  ( 3, 100 ) .] To determine

To calculate: The average inventory per month for the first 3 months where how an inventory of a product is depleted each quarter of a given year is shown by the figure. Explanation

Given information:

The provided figure is:

Formula used:

Equation of line:

The equation of a line passing through the points (x1,y1) and (x2,y2) is given as:

(yy1)=y2y1x2x1(xx1)

Average value

The average value of a continuous function y=f(x) over the interval [a,b] is:

Average value=1baabf(x)dx

Calculation:

Consider the figure:

The average inventory per month for the first 3 months is to be calculated.

This inventory is given by the equation which passes through (0,1300) and (3,100)

Consider the formula:

(yy1)=y2y1x2x1(xx1)

Substitute 1300 for y2, 100 for y1, 3 for x1 and 0 for x1 in above equation to get:

(y100)=130010003(x3)y100=12003(x3)y=400x+1200+

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