   Chapter 7.9, Problem 33E ### 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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# Average Revenue A company sells two products whose demand functions are given by x 1 = 500 − 3 p 1     and     x 2 = 750 − 2.4 p 2 . The total revenue is given by R = x 1 p 1 + x 2 p 2 . Estimate the average revenue when price p1 varies between $50 and$75 and price p2 varies between $100 and$150.

To determine

To calculate: The average revenue of company sell two product p1 varies between $50 and$75 units and p2 varies between $100 and$150 units.

Explanation

Given information:

The average revenue R=x1p1+x2p2 of company sell two product x1 and x2 that demand varies as x1=5003p1 and x2=7502.4p2, where p1 varies between $50 and$75 units and p2 varies between $100 and$150 units.

Formula used:

The average value of integrable function z=f(x,y) over the region R with area A is

Average value=1ARf(x,y)dxdy

Calculation:

Consider revenue function of company,

R=x1p1+x2p2

Here x1=5003p1, x2=7502.4p2 and. Where p1 varies between $50 and$75 units and p2 varies between $100 and$150 units.

Substitute, 5003p1 for x1 and 7502.4p2 for x2 in revenue function,

R=(5003p1)p1+(7502.4p2)p2=500p13p12+750p22.4p22

The area of region between p1 varies between $50 and$75 units and p2 varies between $100 and$150 units is 1250 units.

Now apply, the formula of the average value of integrable function R=500p13p12+750p22.4p22 with p1 varies between $50 and$75 units and p2 varies between $100 and$150 units is 1250 units.

Average value=112501001505075(500p13p12+750p22

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