1. (50) At Bob's Burgers, each burger consists of exactly two buns :t, one meat patty y. and one slice of cheese 2. Let P denote the price of burgers and pm, py, pz be the prices of each input and consider Bob's prot maximizatiOn problem. (a) (10) Write Bob's production function q = f (x, y,z), show that it exhibits constant returns to scale, and nd the marginal products to each factor. (b) (10) Set up Bob's cost minimizatiOn problem, write the Lagrangian E, and show why you cannot use the rst order conditions to solve it. (c) (10) Solve for Bob's cost function C(q)1 and nd the average cost AC(q) and marginal cost M C (q) functions. ((1) (10) Set up Bob's prot maximizatiOn problem, nd the rst order condition. (e) (10) Find the quantity of burgers that Bob Supplies q(P), and nd much prot he earns 71