   Chapter 7.9, Problem 32E ### 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 Weekly Profit After a change in marketing, the weekly profit of the firm in Exercise 31 is given by P = 200 x 1 + 580 x 2 − x 1 2 − 5 x 2 2 − 2 x 1 x 2 − 7500. Estimate the average weekly profit when x1 varies between 55 and 65 units and x2 varies between 50 and 60 units.

To determine

To calculate: The average weekly profit P (in dollars) in marketing two product is given by P=200x1+580x2x125x222x1x27500 when x1 varies between 40 units and 50 units and x2 varies between 45 units and 50 units.

Explanation

Given information:

The average weekly profit P (in dollars) in marketing two product is given by P=200x1+580x2x125x222x1x27500

Where x1 and x2 represent the number of units of each product sold weekly.

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 equation of function,

P=192x1+576x2x12x222x1x25000

Here x1 varies between 55 units and 65 units and x2 varies between 50 units and 60 units.

The area of region is 100 units.

Now apply, the formula of the average value of integrable function P=200x1+580x2x125x222x1x27500 with x1 varies between 55 units and 65 units and x2 varies between 50 units and 60 units is

Average value=110050605565(200x1+580x2x125x222x1x27500)dx1dx2=11005060[100x12+580x2x1x1335x1x22

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