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): = COLC1C2 CO, C11 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. where and = (a) In this example, assume co 5, C 1 = 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. 90,000 L, C O (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.) at (L, C) =