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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Revenue A company manufactures running shoes and basketball shoes. The total revenue from x 1 units of running shoes and x 2 units of basketball shoes is

R   =   5 x 1 2     8 x 2 2 2 x 1 x 2 +   42 x 1 +   102 x 2 where x 1  and  x 2 are in thousands of units. Find x 1  and  x 2 so as to maximize the revenue.

To determine

To calculate: The values of x1 and x2 to maximize the revenue if the total revenue from x1 units of running shoes and x2 units of basketball shoes is provided by R=5x128x222x1x2+42x1+102x2.

Explanation

Given Information:

The total revenue from x1 units of running shoes and x2 units of basketball shoes is provided by R=5x128x222x1x2+42x1+102x2.

Formula used:

If the function y=f(x) has a maximum at a point then their first partial derivatives fx(x) and fy(x) at that point are zero.

Calculation:

Consider the total revenue,

R=5x128x222x1x2+42x1+102x2

Now, the first partial derivatives are,

Rx1=x1[5x128x222x1x2+42x1+102x2]=10x12x2+42=2(5x1x2+21)

And,

Rx2=x2[5x128x222x1x2+42x1+102x2]

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