2. Suppose a local cake factory has a production function of Q = 5√�L. Q is the number of cakes made each day when the firm rents K units of capital and employs L workers each day. The factory makes 50 cakes every day. The daily rental price of capital (r) is $160 per machineday. The wage rate (w) paid to each worker is $40 per person-day. Short run (capital is fixed at 4 machine-days) a. In the short run the capital is fixed at 4 machine-days, find the total cost equation as a function of output Q. (4 points) b. How much is the daily total cost ($) to achieve the target of 50 cakes? (2 points) c. Is the factory optimizing production in the short run? If not, which of the input should the factory increase? (4 points) Long run d. In the long run, how much K and L would be optimal to minimize the cost of making 50 cakes each day? (You can solve the problem with any method you want) (6 points) e. How much money is lost currently in the short run by not operating optimally? (4 points) f. What type of returns to scale is this production? How does the long run marginal cost change with output? (4 points)