00:01
A stadium will hold 55 ,000 spectators.
00:03
When we charge $10, we get 24 ,000 people in the stands.
00:07
If we increase, i mean, if we decrease it total by $1, so it means 9, then we're going to increase the attendance by 2 ,000, so that would be 26 ,000.
00:20
So we want to find the price that will maximize the revenue.
00:24
So we're going to look at this as ordered pairs and find our demand function.
00:28
So let's go ahead and subtract these to get negative 2 ,000.
00:32
Subtract these to get 1.
00:34
So when i get my demand function, which will be linear, i'm going to have y equals negative 2 ,000x plus b.
00:42
Now let's use an order pair to find out what b is.
00:46
I like this one.
00:47
It has more zeros.
00:49
24 ,000 equals negative 2 ,000 times 10 plus b.
00:54
That would be negative 20 ,000, which i can add to this side to get my value of b to be 44 ,000.
01:04
So my equation is going to be negative 2 ,000x plus 44 ,000.
01:11
Now let's look at our revenue.
01:12
Our revenue is going to be the cost of the ticket, which is x, times the number of tickets, which is negative 2 ,000x plus 44 ,000.
01:22
Let's make that negative 2 ,000x squared plus 44 ,000x.
01:28
Now we want to get the maximum.
01:30
So i'm going to get my vertex, negative b over 2a.
01:34
That's a negative and a 2...