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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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Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com

Use the Cobb-Douglas production function in Example 4 to find the production levels when x = 1500 and y = 1000 and when x = 1000 and y = 1500. Use your results to determine which variable has a greater influence on production.

To determine

To calculate: The production levels for the model f(x,y)=100x0.6y0.4 where x is the labor and y is the capital at x=1500, y=1000 and x=1000, y=1500 and also estimate the variable that has greater influence on production.

Explanation

Given Information:

The model for the production levels is f(x,y)=100x0.6y0.4 and the variables are x=1500, y=1000 and x=1000, y=1500.

Calculation:

Consider the model for the production levels, f(x,y)=100x0.6y0.4

For first variable:

Substitute 1500 for x and 1000 for y.

f(1500,1000)=100(1500)0.6(1000)0.4127542.4

For first variable:

Substitute 1000 for x and 1500 for y.

f(1000,1500)=f(1000,1500)=100(1000)0

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