Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL= K¹/² / 2L¹/² & MPK = L¹/² / 2K ¹/²
If the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire to minimize the cost of production if the firm wants to produce output Q = 18?