Assume that a firm has the following production function: Q=30K^1/3 L^2/3, where K is the number of machines and L is the number of hours of labor. The firm has 8 machines it purchased at a price of $50 each and it will be unable to obtain any more machines for the relevant time period. The firm's output sells at a price of $2 per unit, and labor costs the firm $20 per hour.
a) Whats the firm's VMPL function?
b) How many hours of labor should the firm employ?
c) What will be the firms total profit?