If exactly 220 people sign up for a charter flight, leisure world travel agency charges $282/person. however, if more than 220 people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 220. determine how many passengers will result in a maximum revenue for the travel agency. hint: let x denote the number of passengers above 220. show that the revenue function r is given by r(x)

251 passengers will result in a maximum revenue.

Step-by-step explanation:

The price per ticket of the first 220 passengers is given by:

The price per ticket of the additional x passengers is:

Adding both parts gives us the revenue function R(x):

The term (282-x) is present in both parts and can be factored:

To find how many passengers will result in a maximum revenue, derive the function R(x) and find its zeroes:

31 passengers above 220 will result in a maximum revenue. Therefore, 251 passengers will result in a maximum revenue.