3. Suppose a competitive rm's production function is q = LD'5KD'5 and the wage rate is m = $5 and the rental rate is r = $0.8. (a) If K is xed at 25 units in the short-run, what is the short-run production function? (b) What is the equation that determines how much labor the rm should hire to produce some quantity, (1? (c) Use your answer to (b) to derive the short-run total cost curve. (d) What is the rm's marginal cost curve? What is the rm's average total cost curve? (e) If the price of the rm's product is $6, how man}.r units should the rm choose to sell? (f) What are its short-run prots? Provide a diagram that illustrates the rm's optimal choice of q and its prots. You will need a marginal cost curve, average total cost curve, and marginal revenue (equals price) line. (g) Based on your answer to (f), how do you know the rm is n_ot operating in the long-run