2. Suppose that the production of sports cars is given by the following production function: Q = (11/2 4 K1/2)2 Suppose that the price of labor is $10 per unit and the price of capital is $1 per unit. a. Find the optimal labor and capital combination as a function of output Q. b. Derive the firm's long-run total cost function. c. Derive the firm's long-run average total cost function. d. Does the firm experience economies of scale or diseconomies of scale? If so, at what ranges? If not, why not? e. Derive the firm's long-run marginal cost function. f. Find the cost-minimizing combination of labor and capital for a sports cars' manufacturer that wants to produce 121,000 sports cars