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
765
876
To find the revenue function R(x), we need to first determine the total number of passengers, which is given by 198 + x, where x is the number of passengers above 198.
The fare per person is $308 with exactly 198 people signing up. If more than 198 people sign up, the fare per person is reduced by $1 for each additional person. The fare per person can be represented as $308 - $1 * x.
The revenue function is calculated by multiplying the total number of passengers by the fare per person:
R(x) = (198 + x) * (308 - x)
To determine the number of passengers that will result in a maximum revenue, we need to find the maximum point of the revenue function. This can be done by taking the derivative of R(x) with respect to x, setting it equal to zero, and solving for x:
dR(x)/dx = -x^2 + 110x + 61184 = 0
To solve this quadratic equation, we can use factoring, completing the square, or using the quadratic formula. Once we find the value of x, we can substitute it back into the revenue function to find the maximum revenue.
To find the fare per passenger in this case, we can substitute the value of x that results in the maximum revenue into the fare equation: $308 - $1 * x. This will give us the fare per passenger.