A real estate company manages 150 apartments in Irvine, California. All the apartments can be rented at the price of $1,200 per month, but for every $100 increase in the monthly rent, there will be 5 additional vacancies.
a) Express the total monthly revenue R obtained from renting apartments as a function of the monthly rental price p for each unit.
b) What price should the company charge in order to maximize total revenue? What is the maximum revenue?