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) = c₀ L^C₁ C^C₂

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.

1. In this example, assume c₀ = 4, c₁ = 0.75, and c₂ = 0.25. 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. If your answer is zero enter "0".
2. 

Max s.t. LC ted in part (a). Hint: Put bound constraints on the variables based on the budget constraint. Use LS 3000 and CS 1000 and use the Multistart option as described in Find the optimal solution to the model you Appendix 8.1. Round your answer for optimal solution to mal place, if needed. L = and C = for mal objective function value of > =