0:00
All right, hello.
00:01
In this question, we are going, we're asked to write an equation for the revenue of an airline service and figure out what the maximum revenue they can make is.
00:11
And so, reading the question through, if exactly 200 people sign up for a charter flight, the operators of the charter airline charge $300 for a round -trip ticket.
00:22
So we know that if n, the number of people, is equal to 200, they're going to charge a cost of $300 per ticket.
00:34
However, if more than 200 people sign up for the flight, so if n is greater than 200, then each fare is reduced by $1 for each additional person.
00:48
So what does that mean? that means we're going to charge $300, but we're going to subtract $1 for each additional person.
00:57
So we say if we have 201 people, we want it to be $1 .99.
01:02
202, we want it to be minus $2.
01:05
So we're going to have 200, or sorry, we're going to have the number of people, the number of tickets n, minus 200.
01:14
And just check to make sure this works.
01:16
If we had, say, five people, we know that the cost should be $295.
01:22
So if we have 205, five extra people over 200, we'll end up with this.
01:28
So we have five, 300 minus five, that is what we want.
01:32
So this is our cost of the ticket.
01:36
And we're asked to maximize revenue.
01:38
And so we assume revenue, there's no operating costs here, or they're just fixed, it doesn't matter how many they sell.
01:45
So their revenue for some number of tickets is going to just be the cost, and that's going to be in dollars per ticket times the number of tickets.
01:57
And if we cancel out, we'll just end up with dollars.
02:00
So r of n in this case is going to be 300.
02:04
And i'm going to simplify this here a little bit and say that that's minus n plus 200.
02:12
And that's just going to be times the number of tickets sold.
02:15
So expanding that out will look something like 500n plus n squared...