00:01
So in this problem, we're given a couple facts about the relationship between the cost of airline tickets and how many tickets are sold.
00:07
So, for instance, we're told that at 10 ,000, that at a price of 200, 10 ,000 tickets are sold.
00:16
So we can write an equation starting in point slope form.
00:20
We can say the number of tickets sold, s minus 10 ,000, is going to be proportional, some factor, is going to be proportional to the price.
00:31
Minus 200.
00:32
So if the price is equal to 200, if this is equal to zero, then this side will be equal to zero and we'll sell 10 ,000 tickets.
00:41
And we're given this proportionality.
00:43
We're told that for every decrease of 35, we sell 1 ,000 more tickets and a minus sign because of the decrease.
00:53
So if p minus 200 is negative 35, we'll get an increase of 1 ,000.
01:01
So right away, this is a point slope form equation for relating the number of tickets sold to the current price of a ticket.
01:10
And now we can set a profit that the airline makes from selling these tickets because we know that the money they're going to take in is going to be equal to the number of tickets sold times the profit that they make times the price of each ticket that they bring in minus 100, because it costs them $100 to fly each person on the plane...