Suppose the production function is given by Q=2L^1/4 K^1/4 , price of labor (w)=3 and price of capital (r)=12. The market price for the output produced is P=54. Answer parts a(i)−a(iv) and b(ii) to b(vi) based on this information. Short-rum production: Suppose capital is fixed at K=81. i. Write down and solve this firm's SHORT-RUN cost minimization problem. [Note: Capital is fixed here, so the firm chooses only labor to minimize cost.] Find out the short-run cost of the firm for producing 24 units of output. ii. Write down the functional forms of the short-run average total cost, average variable cost and marginal cost. Draw them in a diagram. iii. Find out the profit maximizing choice of output and labor in the short-run. How much is the profit?