3. A firm's production function is given by f( L, K) - L3Ks. The per-unit cost of capital is r and the per-unit cost of labor is w. (a) Set up the Lagrangian for the firm's cost-minimization problem. (5 points) (b) Solve for the firm's conditional factor demands, L(w, r, y) and K(w, r, y). (5 points) (c) Solve for the firm's cost function, C(w, r, y). (5 points) (d) What is the minimum cost required to produce 20 units of output if r = w = 10? (5 points)