If exactly 198 people sign up for a charter flight, Leisure World Travel Agency charges $308/person. However, if more than 198 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Hint: Let x denote the number of passengers above 198.
Find the revenue function R(x).
R(x) = ?
Determine how many passengers will result in a maximum revenue for the travel agency.
? passengers
What is the maximum revenue?
$ ?
What would be the fare per passenger in this case?
? dollars per passenger
To find the revenue function R(x), we need to determine the total revenue generated based on the number of passengers above 198.
When exactly 198 people sign up, each person is charged $308. So the revenue from these 198 people is:
198 people * $308/person = $60,984
Now, let's consider the case where more than 198 people sign up for the flight. For each additional person, the fare is reduced by $1. So, if there are x passengers above 198, the fare per person becomes $308 - $1 * x.
The total number of passengers in this case would be 198 + x, and the revenue from these passengers would be:
(198 + x) * ($308 - $1 * x)
Therefore, the revenue function R(x) = (198 + x) * ($308 - $1 * x).
To determine the number of passengers that will result in maximum revenue for the travel agency, we need to find the value of x that maximizes the revenue function R(x).
To find the maximum of a quadratic function like R(x), we can use calculus. We need to find the critical points by taking the derivative of R(x), setting it equal to zero, and solving for x.
To find the maximum revenue, we substitute the value of x that maximizes the revenue into the revenue function R(x) and calculate the maximum revenue.
Finally, to find the fare per passenger in this case, we divide the maximum revenue by the total number of passengers (198 + x).
By following these steps, we can find the answers to the given questions.