Chapter 4.5, Problem 19E

Optimal Charter Flight Fare If exactly 200 people sign up for a charter flight. Leisure World Travel Agency charges $300/person. However, if more than 200 people sign up for the flight (assume that this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result m a maximum revenue for the travel agency. What is the maximum revenue? What would be the fare per passenger in this case?

Hint: Let x denote the number of passengers above 200. Show that the revenue function R is given by R(x) = (200 + x) (300 − x).