What are the quantities of two inputs the firm must buy in order to produce a maximum output, given input and budget constraints?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 53P
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A firm buys two inputs, labor L and capital K, the total amount of which cannot exceed 100 units. The wage is $8, and the rental rate of
capital is $10. The firm can, at most, spend $840 on the two inputs.
This data can be summarized in the following equations:
Input limit: K +L = 100
Budget limit: 8L + 10K = 840
What are the quantities of two inputs the firm must buy in order to produce a maximum output, given input and budget constraints?
K =
Transcribed Image Text:A firm buys two inputs, labor L and capital K, the total amount of which cannot exceed 100 units. The wage is $8, and the rental rate of capital is $10. The firm can, at most, spend $840 on the two inputs. This data can be summarized in the following equations: Input limit: K +L = 100 Budget limit: 8L + 10K = 840 What are the quantities of two inputs the firm must buy in order to produce a maximum output, given input and budget constraints? K =
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