A firm employs a Cobb-Douglas production function of the form y = K4L04. The output price is p and the input prices are r and w for K and L, respectively. (a) Set up the problem for a profit maximizing firm and solve for the demand function for both inputs. (b) Show the first order and the second order condition for profit maximization. (c) Derive the profit function. (d) Are K and L substitute or complements?