Fairway Chemicals manufactures fertilizer for golf courses. The production function for a particular brand of fertilizer is Q = min[3P,N], where Q is pounds of fertilizer, P pounds of phosphate, and N pounds of nitrogen.

a. What is the marginal product of phosphate?

b. What is the marginal product of nitrogen?

c. Suppose that the prices of phosphate and nitrogen are $1.50 and

$4.50, respectively. Suppose that Fairway has budgeted $90,000 to produce this brand. How much phosphate and nitrogen will Fairway purchase to maximize total output?

d. How much of this brand of fertilizer should Fairway produce?

e. What is Fairway’s profit from this brand of fertilizer if the price is

$5 per pound?