A company has the Cobb-Douglas production function z = :400x0.6 where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose labor costs Php 2000 per unit, capital costs Php 4000 per unit, and the total cost of labor and capital is limited to Php 1,000,000. Use the method of Lagrange Multipliers to solve the following problems. 1) Find the number of units of labor and the number of units of capital that maximize production. 2) How much should be allocated to labor and capital to maximize production? 3) What is the maximum production?

A company has the Cobb-Douglas production function z = :400x0.6 where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose labor costs Php 2000 per unit, capital costs Php 4000 per unit, and the total cost of labor and capital is limited to Php 1,000,000. Use the method of Lagrange Multipliers to solve the following problems. 1) Find the number of units of labor and the number of units of capital that maximize production. 2) How much should be allocated to labor and capital to maximize production? 3) What is the maximum production?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 10E

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