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) = co LC: C2 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 - 6, c1 = 0.75, and c2 - 0.25. Assume each unit of labor costs $25 and each unit of capital costs $75. With $85,000 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. If your answer is zero enter "0". Маx s.t. L, C b. Find the optimal solution to the model you formulated in part (a). Hint: Put bound constraints on the variables based on the budget constraint. Use L s 3000 and Cs 1000 and use the Multistart option as described in Appendix 8.1. Round your answer for optimal solution to one decimal place, if needed. and C - for an optimal objective function value of

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) = co LC: C2 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 - 6, c1 = 0.75, and c2 - 0.25. Assume each unit of labor costs $25 and each unit of capital costs $75. With $85,000 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. If your answer is zero enter "0". Маx s.t. L, C b. Find the optimal solution to the model you formulated in part (a). Hint: Put bound constraints on the variables based on the budget constraint. Use L s 3000 and Cs 1000 and use the Multistart option as described in Appendix 8.1. Round your answer for optimal solution to one decimal place, if needed. and C - for an optimal objective function value of

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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