If exactly 150 people sign up for a charter flight, Leisure World Travel Agency charges $250/person. However, if more than 150 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in 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 150. Show that the revenue function R is given by R(x) = (150 + x)(250 - x).

Question

Quizplus · Accepted Answer

The revenue function is R(x) = (150 + x)(250 - x). To find the maximum revenue, take the derivative and set it to zero to find x = 50. Thus, the total number of passengers is 200, the fare per passenger is $200, and the maximum revenue is $40,000.

If Exactly 150 People Sign Up for a Charter Flight