   Chapter 7.9, Problem 31E ### 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 A firm’s weekly profit P (in dollars) in marketing two products is given by P = 192 x 1 + 576 x 2 − x 1 2 − 5 x 2 2 − 2 x 1 x 2 − 5000 where x1 and x2 represent the numbers of units of each product sold weekly. Estimate the average weekly profit when x1 varies between 40 and 50 units and x2 varies between 45 and 50 units.

To determine

To calculate: The average weekly profit P (in dollars) in marketing two product is given by P=192x1+576x2x12x222x1x25000 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=192x1+576x2x12x222x1x25000.

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 40 units and 50 units and x2 varies between 45 units and 50 units.

The area of region is 50 units.

Now apply, the formula of the average value of integrable function P=192x1+576x2x12x222x1x25000 with x1 varies between 40 units and 50 units and x2 varies between 45 units and 50 units with area 50 units is

Average value=15045504050(192x1+576x2x12x222x1x25000)dx1dx2=1504550[96x12+576x2x1x1335x1x22x

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