The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = CL²1C 2 where Co, C₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co= 5, C₁ = 0.25, and c₂ = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. L, C ≥ 0 ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when necessary.)

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = CL²1C 2 where Co, C₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co= 5, C₁ = 0.25, and c₂ = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. L, C ≥ 0 ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when necessary.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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