00:03
Right, we're building a fenced -in area.
00:06
The area has to be 10 square meters, and it's x by y, are the dimensions of this region here.
00:16
But for the side that has the x, half of it is missing.
00:19
In other words, we have an opening to get into this fenced -in area here.
00:24
We want to minimize the amount of fence that's needed to do this.
00:28
All right, so let's think about what is it that we need to minimize.
00:31
We need to minimize the fence.
00:33
Well, the fence is really just the perimeter.
00:35
So i'm just going to write perimeter.
00:36
And we know how to find the perimeter.
00:38
That's going to be i have two ys.
00:41
And normally i would have two full x's, but in this case, i only have one and a half x.
00:47
So i'll write that as plus three halves x.
00:50
So that's my perimeter.
00:51
That's what i'm trying to minimize.
00:53
So what we're going to do is we're going to find the change in this thing with respect to one of these variables and then find our critical values by setting it equal to zero and so on.
01:03
But right now i have two separate variables here.
01:05
So what we need to do is write one of them in terms of the other.
01:09
And that's why we have the secondary information up here.
01:12
All right, we haven't used the fact that the area has to be 10 square meters.
01:15
We know how to find the area of this.
01:17
That's simply x times y.
01:19
And that's pretty easy now to solve for one in terms of the other.
01:24
It's not really going to make much of a difference which one we solve for.
01:26
When i substitute in, i just have to multiply by it.
01:28
And here, either way, it's going to be 10 divided by the other one.
01:31
So i'll just solve it for one.
01:33
So y is equal to 10 divided by x.
01:37
All right.
01:37
So now i come back to what it is that i'm trying to minimize, and i do 10 times.
01:41
But instead of y, i'm going to write 10 divided by x and then plus three halves x.
01:49
All right...