You are a manager for Herman Miller - a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is:
Q = 2K^(0.5) L^(0.5)
where K represents capital equipment and L is labor. Your company owns 4 units of capital equipment and does not have the flexibility needed to acquire additional equipment (that is, capital is fixed at K = 4). Your company is currently employing 25 units of labor.

a. calculate the following:
i. Average product of labor

ii. Marginal product of labor

iii. Marginal product of capital

iv. Marginal rate of technical substitution.

b. Workers at the firm are paid a competitive wage of $100 and chairs are sold for $200 each.
i. Calculate value marginal product of labor (VMPL).

ii. Is your company currently employing the profit-maximizing level of labor? Why or why not?

iii. How many units of labor should your firm normally employ in order to maximize profits?