申論題

2. Suppose that the production P depends on the amount L of labor used and the amount K of capital invested, for some constant a, 0 ＜ a ＜ 1. Assume that the cost of a unit of labor is 20 thousand dollars and the cost of a unit capital is 50 thousand dollars. If a company can spend C thousand dollars as its budget, then the company seeks the maximum production subject to the constraint 20L + 50K = C.

(a) Solve for the max um production,, in terms of C and a.