A firm's production is represented by the following function: Q = L^0.4 K ^0.6 . The rental rate of capital (r) is $30 and the wage rate (w) is $5.

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 600 units of output? What is the total cost?

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

d. What would be the optimal choice of capital and labor in the long run in order to produce 300 units of output? What is the long-run total cost?

e. Does this production function exhibit increasing, decreasing, or constant returns to scale? Please answer based on the cost calculations in parts c and d.