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Afirm has the production function Q : 4K0'5L0'5. The wage rate is $80 and the rental rate is $20. a. (4pt) Find the short-run total cost curve of this firm when K is fixed at 25 units. b. (12pt) Find the optimal amount of inputs (K and L) the firm uses in the |o_ng-run. Hint: K is no longer fixed. You might want to use the Lagrangian method to answer this question. Your answers to this question will be in terms of 0 since you are finding the optimal amount of inputs for any quantity that rm might choose to produce. c. (4pt) Find the |o_ng-run total cost curve of the firm. Hint: Even if you can't find the answer for part b, you can get points for explaining how you would answer this part. d. (4pt) Does the firm exhibit economies of scale, diseconomies of scale, or constant economies of scale? Why? Hint: Even if you can't find the answer for part c, you can get points for explaining how you would answer this part