(50) At Bob's Burgers, each burger consists of exactly two buns r, one meat patty y, and one slice of cheese z. Let P denote the price of burgers and Pr, Py, pz be the prices of each input and consider Bob's profit maximization problem. (a) (10) Write Bob's production function q = J(r, y, z), show that it exhibits constant returns to scale, and find the marginal products to each factor. (b) (10) Set up Bob's cost minimization problem, write the Lagrangian C, and show why you cannot use the first order conditions to solve it. (c) (10) Solve for Bob's cost function C(q), and find the average cost AC(q) and marginal cost MC(q) functions. (d) (10) Set up Bob's profit maximization problem, find the first order condition. (e) (10) Find the quantity of burgers that Bob supplies q(P), and find much profit he earns