2) The total - cost and total - revenue, in dollars, of
producing and selling x units of a certain product are given by:
R(x) = 1000x -x^2 and C(x) = 3000 + 20x
a. Find the total profit function, P(x)
b. Use the second derivative test to determine how many units,
x, must the company produce and sell in order to maximize the
profit?
c. What is the maximum profit?
d. If the price per unit is given by p(x) = 1000 - x, what price
per unit must be charged in order to make this maximum profit?