A firm's production function is: Q = 6K1/3 L 2/3 and capital is fixed at 125 units. The firm can sell its output at a price of $200 per unit, hire labor at $20 a unit, and rent capital at $40 a unit.

a. Determine the optimum level of labor and output to maximize profits.

b. Calculate the level of profits at the profit-maximizing level of labor and output given that capital is fixed at 125 units.

c. Briefly discuss the concept of diminishing returns and why it is important to understand this concept as a manager.

d. Why, as a manager, it is important to understand the relationship between average costs, marginal costs, average productivity, and marginal productivity?