3. (30 total points) Suppose a firm's production function is given by Q = L^1/2*K^1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by:

MP_L = K1/2 over 2L 1/2 and MP_K = L1/2 over 2k1/2

a) (12 points) 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 in order to minimize the cost of production if the firm wants to produce output Q = 10?

b) (12 points) What is the firm's Total Cost function TC(Q)?

c) (6 points) What is the firm's marginal cost of production?

4. (20 total points) Suppose in the short run a perfectly competitive firm has variable cost = 3q², and MC = 6q where q is the quantity of output produced.Also, the firm has fixed cost F = 3000.

a) (8 points) If the market price of the product is 180, how much output should the firm produce in order to maximize profit?

b) (6 points) How much profit will this firm make?

c) (6 points) Given your answer to b), what will happen to the market price as we move from the short run to the long run?