A catfish processing firm has the following production function:

Q= 12L -1/3L² +18K- 2/5K²

a. What is the firm's marginal product of labor? What is the marginal product of capital?

b. Assume the firm uses labor and capital in the range of 0 to 10 units. Does the firm experience diminishing marginal returns for both inputs?

c. What returns to scale does the firm's production function have?

d. The average wage per hour for workers at the catfish processer are $16 and the price of capital is $26. Provide the relationship between these two inputs at the optimal, least cost mix.