Question: A firm can sell X units of a product at a price of P cents per unit, where P = 503 - X
The total costs of production is given by the function T(X) = 500 + 2X

a. Find the function that relates total revenue to the number of units sold - R(X).

b. Find the function that relates total profit to the number of units sold - P(X).

c. Find the number of units to be sold to achieve maximum profit and find the maximum profit.

d. What price per unit would the firm be charging at the maximum profit output level?