12. A firm's production is represented by the following function: Q = L1/4 K 3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.

a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?

b. How much capital and labor should be used to produce 400 units of output? What is the total cost?

c. What is the short run total cost if output is decreased to 300 units?

d. How would the capital labor choice and total cost change in the long run? e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternative location assuming relocation is costless?