Question: A firm determines that x units of its product can be sold daily at p dollars per unit where x = 1000 – p. The cost of producing x units per day is

C(x) = 3000 + 20x. (Hint: FIRST solve x = 1000 – p, for p in terms of x)

(a) Find the revenue function, R(x).

(b) Find the profit function, P(x)

(c) Assuming that the production capacity is at most 500 units per day, determine how many units the company must produce and sell each day to maximize the profit.

(d) Find the maximum profit.

(e) What price per unit must be charged to obtain the maximum profit?