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Question 6. Optimal Input Decisions [20 Marks] A furniture firm has calculated the following production function, relevant for their long-run capital-labor decisions. Q = 3L1/3K2/3, where Q = annual output measured in pounds, L = labor measured in person hours, K = capital measured in machine hours. Each craftsman is highly skilled and earn f18 per hour. The furniture firm estimates a rental charge of 190 per hour on capital, and predicts an annual cost of f270,000 per year, measured in real Pounds. (a) Do the production function exhibits increasing, constant, or decreasing returns to scale? Explain your answer (mathematical demonstration). [4 marks] (b) What are the marginal products of labor (MP,) and capital (MPR)? Determine the firm's optimal capital-labor ratio, given the information above. [7 marks] (c) Construct the isocost equation. How much capital and labour should the firm employ, given the f 270,000 budget? [7 marks] (d) Calculate the firm's output at the optimal production situation. [2 marks]