Problem 8-07 (Algorithmic) 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 LC1 C2 where co, ci, 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 = 8, C1 = 0.75, and c2 = 0.25. Assume each unit of labor costs $75 and each unit of capital costs $25. With $50,000 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". Max L s.t. L C 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 C s 1000 and use the Multistart option as described in Appendix 8.1. Round your answer for optimal solution to one decimal place, if needed. L = and C= for an optimal objective function value of