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A company has the Cobb-Douglas production function z = 400x0.6 0.4 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 1500 per unit, capital costs Php1000 per unit, and the total cost of labor and capital is limited to Php5,000,000. 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

A company has the Cobb-Douglas production function z = 400x0.6 0.4 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 1500 per unit, capital costs Php1000 per unit, and the total cost of labor and capital is limited to Php5,000,000. 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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A company has the Cobb-Douglas production function z = 400x0.6 y0.4 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 1500 per unit, capital costs Php1000 per unit, and the total cost of labor and capital is limited to Php5,000,000. 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?
Transcribed Image Text:A company has the Cobb-Douglas production function z = 400x0.6 y0.4 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 1500 per unit, capital costs Php1000 per unit, and the total cost of labor and capital is limited to Php5,000,000. 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?
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