00:01
Hello.
00:03
This problem is about an ice cream company for which we read carefully when the price is $4 .00.
00:16
The demand is 4 ,000 units.
00:25
And for every change in p of minus 1 .25, we have a change in q.
00:39
Of plus 200 units.
00:44
Alright.
00:49
The demand function, assuming that is linear, let's have a little bit linear function as well and y is a linear function of x, then we have mx plus some y interstate b, and this m is calculated as a difference in y, the change in y, over the change of x.
01:14
So we are going to either show p as a function of q or q as a function of p.
01:20
Let's go for pq.
01:23
Let's show quantity as a function of price.
01:28
We can go either way.
01:31
Right, so we have a point on the graph.
01:34
We have a point in the graph.
01:35
Pq for 4 ,000, 1000, and we are given the...
01:43
We are given the slope of...
01:49
Changing, what are we taking for, changing q.
01:56
If i write it like this, then q is a function of p.
02:01
Okay, we'll go that way.
02:02
We'll find what is the q as a function of p.
02:08
So we'll take delta q through delta p, which is 200 over minus 0 .25.
02:20
Okay, this calculator gives us 800 minus 800.
02:31
Now we use the point slope, form of the equation of a line.
02:40
This was p, this was q.
02:42
So we have q minus q1, which is 4 ,000, is equal to m, which is minus 800.
02:52
That multiplies p minus p .1 is 4.
02:57
The equation i used is y minus y1 equals m x minus x1 points level.
03:07
Okay, transferring this over the other side, q will be equal to minus 800p plus 3 ,200 and an additional 4 ,000 derived from the other side and we added here.
03:27
So it's minus, kiwi is minus 800 plus 7 ,200.
03:38
Phew, okay.
03:41
Okay.
03:53
The question we need to answer, just to point out, is to find, is to find, the price and quantity sold, the price and quantity sold when the revenue is maximized...