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) = coLCICCZ where co, cl, and 52 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 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $70,000 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. 5 70,000 L,CZO (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 s L 5 3,000 and 0 s C 5 1,000. Round your answers to the nearest integer when necessary.) units at (L, C) =