Essentials of Business Analytics 1st Edition by Jeffrey Camm,James Cochran,Michael Fry,Jeffrey Ohlmann ,David Anderson

Exercise 1

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

where c 0 , c 1, and c 2 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 c 0 5 5, c 1 5 0.25, and c 2 5 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $75,000 available in the budget, develop an optimization model to determine how the budgeted amount should be allocated between capital and labor in order to maximize output.
b. Find the optimal solution to the model you formulated in part a. ( Hint: When using Excel Solver, use the Multistart option with bounds 0 # L # 3000 and 0 # C # 1000.)