Q. No. 1: A company has determined that its production level is given by Cobb-Douglas function f(x, y) = 2.5x0.45y0.55 where x represents the total number of labor hours in 1 year and y represents the capital input for the company. Suppose 1 unit of labor costs $40 and l unit of capital costs $50. Use the method of lagrange multipliers to find the maximum value of f(x, y) = 2.5x0.45y0.55 subject to a budgetary constraint of $500,000 per year.

Q. No. 1: A company has determined that its production level is given by Cobb-Douglas function f(x, y) = 2.5x0.45y0.55 where x represents the total number of labor hours in 1 year and y represents the capital input for the company. Suppose 1 unit of labor costs $40 and l unit of capital costs $50. Use the method of lagrange multipliers to find the maximum value of f(x, y) = 2.5x0.45y0.55 subject to a budgetary constraint of $500,000 per year.

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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Question

Q. No. 1: A company has determined that its production level is given by Cobb-Douglas function
f(x, y) = 2.5x0.45y0.55
where x represents the total number of labor hours in 1 year and y represents the capital input for the
company. Suppose 1 unit of labor costs $40 and 1 unit of capital costs $50. Use the method of
lagrange multipliers to find the maximum value of f(x, y) = 2.5x045y0.55 subject to a budgetary
constraint of $500,000 per year.

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