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

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 to determine how the budgeted amount should be allocated between capital and labor in order to maximize output.

f(L,C) = c,LC