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) = c0Lc1Cc2
where c0, 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 c0 = 5, c1 = 0.25, and c2 = 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 for determining 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: Put bound constraints on the variables based on the budget constraint. Use L ... 3000 and C ... 1000 and use the Multistart option as described in Appendix 8.2.
Text Book: An Introduction to Management Science: Quantitative Approaches to Decision. By David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm, James Cochran.