If exactly 202 people sign up for a charter flight, Leisure World Travel Agency

Question

If exactly 202 people sign up for a charter flight, Leisure World Travel Agency charges $298/person. However, if more than 202 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Let x denote the number of passengers above 202. 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

Explanation / Answer

Solution:

Find the revenue function R(x).

R(x) = (298 - x)* (202 + x)
R(x) = 60196 + 96x - x2

Determine how many passengers will result in a maximum revenue for the travel agency.

dR(x)/dx = 96 - 2x = 0
=> 96 = 2x => x = 48

so total passenger = 202 + 48 = 250

maximum revenue;

R(48) = 60196 + 96*48 - 482 = $62500

What would be the fare per passenger in this case?

F(48) = 298 - 48 = $250

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