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:
MPL = (K^1/2)/(2L^1/2), and MPK= (L^1/2)/(2K^1/2) .
a) If the price of labor is w = 36, and the price of capital is r = 64, 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 = 24?
b) What is the firm's Total Cost function TC(Q)?
c) What is the firm's marginal cost of production?