In internet-based grocery delivery service operates according to the production function Q = K0:5L where K is the number of trucks it uses, L is the number of workers it employs and Q is the number of deliveries. The wage is $6 per hour and the rental price of trucks is $12 per hour. The company currently rents 64 trucks.

a. What are the short run total, average and marginal cost functions (as functions of quantity) of this firm?

b. What are the long run total, average and marginal cost functions (as functions of quantity) of this firm?

c. Does the production function exhibit increasing, decreasing or constant returns to scale?

d. Suppose that the price of 1 unit of output is equal to p: What is the prot maximizing quantity? What are profits?