A manufacturer can produce digital recorders at a cost of $50 apiece. It is estimated that if the recorders are sold for p dollars apiece, consumers will buy q = 120 − p recorders each month.

a. Express the manufacturer’s profit P as a function of q.

b. What is the average rate of change in profit obtained as the level of production increases from q = 0 to q = 20?

c. At what rate is profit changing when q = 20 recorders are produced? Is the profit increasing or decreasing at this level of production?