Question: 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

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 = K^1/2 divided by 2L^1/2 , and MP_K = L^1/2 divided by 2K^1/2 .

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?

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