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 = 18?

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 = , and MP_K = .

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 = 18?

Economics

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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 = 18?

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