Question below:

6. Suppose the production function is given by Q = 2L%K%, price of labor (w) = 3 and price of capital [1") = 12. The market price for the output produced is P = 128. Answer parts a (2') a. (in) and b (2') to 5(1)} based on this information. (a) Short-run production: i. Suppose capital is xed at K = 81. Write down and solve this rm's SHORT-RUN cost minimization problem. [Note: Capital is xed here, so the rm chooses only labor to minimize cost.] Find out the short-run cost of the rm for producing 18 units of output. Partb 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 prot maximizing choice of output and labor in the short-run. How much is the prot