   Chapter 7.9, Problem 35E ### 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 Production The Cobb-Douglas production function for an automobile manufacturer is f ( x , y ) = 100 x 0.6 y 0.4 where x is the number of units of labor and y is the number of units of capital. Estimate the average production level when the number of units of labor x varies between 200 and 250 and the number of units of capital y varies between 300 and 325.

To determine

To calculate: The average production level of Cobb-Douglas production function for for an automobile is f(x,y)=100x0.6y0.4 when x varies between 200 units and 250 units and y varies between 300 units and 325 units.

Explanation

Given information:

The average production level of Cobb-Douglas production function for an automobile is f(x,y)=100x0.6y0.4 when x varies between 200 units and 250 units and y varies between 300 units and 325 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 production level of Cobb-Douglas,

f(x,y)=100x0.6y0.4

Here x varies between 200 units and 250 units and y varies between 300 units and 325 units.

The area of region is 1250 units.

Now apply, the formula of the average value of integrable function f(x,y)=100x0.6y0.4 with x varies between 200 units and 250 units and y varies between 300 units and 325 units.

Average value=11250300325200250(100x0.6y0.4)dxdy=11250300325[(100y0.4)x1

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