A manufacturing company has determined that the number of units of production is determined by the production function f(x, y) = 10x25 y5 %3D where x is the number of units of labor and y is the number of units of eapital used. The cost of labor is $90 per unit and the cost per unit of capital is $70. The company would like to maximize its production given that its total costs cannot exceed $2500. 5 4.1 How many units of labor should the company use?

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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A manufacturing company has determined that the number of units of production is determined by
the production function
f(x, y) = 10x5 3/5
%3D
where x is the number of units of labor and y is the number of units of eapital used. The cost of labor
is $90 per unit and the cost per unit of capital is $70. The company would like to maximize its
production given that its total costs cannot exceed $2500.
5 4.1
How many units of labor should the company use?
Give your answer as a decimal accurate within #0.2% of the exact answer.
Transcribed Image Text:A manufacturing company has determined that the number of units of production is determined by the production function f(x, y) = 10x5 3/5 %3D where x is the number of units of labor and y is the number of units of eapital used. The cost of labor is $90 per unit and the cost per unit of capital is $70. The company would like to maximize its production given that its total costs cannot exceed $2500. 5 4.1 How many units of labor should the company use? Give your answer as a decimal accurate within #0.2% of the exact answer.
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