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{"ops":[{"insert":"Let the production function be given by Q = KL with r = 2 and w = 1. [Note: (marginal product of capital) MPK = L and (marginal product of labor) MPL = K.]\na) How much K and L is employed in the efficient production of 32 units of output?\nb) What is the minimum cost of producing 32 units of output?\nc) Show your results graphically.\n4. Let the production function be given by Q = 2K + L with r = 3 and w = 1. a) How much K and L is employed in the efficient production of 10 units of output? b) What is the minimum cost of producing 10 units of output? c) Show your results graphically. 5. Let the production function be given by Q = min{2K, L} with r = 2 and w = 1.\na) How much K and L is employed in the efficient production of 20 units of output?\nb) What is the minimum cost of producing 20 units of output?\nc) Show your results graphically.\n6. Derive the cost function associated with the production function in questions 2. and 3. The cost function is of the general form C(Q) = xQ. What is the value of x?\n"}]}

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