00:01
Burgers selling for 230.
00:02
They were able to sell 4250, but when they raise the price to 270, they sold for 3250.
00:09
Let's find the demand curve.
00:12
So we're going to first get y equals mx plus b.
00:15
We're going to find our slope.
00:17
So i'm going to subtract.
00:18
So i'm going to say 3250 minus 4250.
00:21
We're looking at negative 1 ,000.
00:23
And then when i subtract here, we're going to get 0 .4.
00:27
So let's see what that's going to be.
00:33
That means my slope is going to be negative 2 ,500 x.
00:38
And now we need to know what b is.
00:41
So i want to come over here then and use one of these ordered pairs.
00:45
It doesn't matter.
00:46
And say, i'll just use the bottom one.
00:48
3250 is going to be negative 2 ,500 times 2 .70 plus b.
00:54
So that means 3250 plus 2 ,500 times 2 .7 is going to be my value of b and that'll be 10 ,000.
01:04
So my demand curve is going to be y equals negative 2 ,500 x plus 10 ,000.
01:12
Now that's not going to be our revenue.
01:14
This is how many we're going to sell or this at a particular price of x.
01:20
So how many are we going to get our revenue? we're going to take the number that we sell the price we sell it at times the number we sell.
01:30
That's our revenue function.
01:33
Now since we're using calculus, i'm going to go ahead and say my r of x is going to be negative 2 ,500 x squared plus 10 ,000 x.
01:42
To find the maximum here, we would take the derivative, which is going to be negative 5 ,000 x plus 10 ,000, set that equal to zero, negative 5 ,000 x equals negative 10 ,000, so x would equal to 2...