00:01
All right, so in this problem, we have a farmer.
00:03
They only have 400 feet of fencing, and they're going to construct this pen or corral.
00:10
There was no pictures, so i'm hoping i get this correct.
00:16
The barn, they don't need any fencing, so where the barn is, no fence.
00:20
So they need fencing here and here.
00:25
Let me do this.
00:29
They need fencing here and here.
00:32
Those are exteriors, and then they have some interior fencing to section it out.
00:37
So there's three air, three spaces.
00:40
And then they need fencing out here.
00:45
So i'm just, instead of having, it's all broken, i'm just called that all of that.
00:49
I'll just call that y.
00:52
Okay, so i know that one, two, three, four x's, four x's plus the y portion where we have fencing has to equal 400.
01:08
Really, it has to be less than 400, but let's use all the fencing we got.
01:13
It has to be, so it should be less than or equal to 400.
01:16
And now i know the area, i'm assuming we want to maximize the area.
01:22
Well, the area is going to just be x times y.
01:25
Okay.
01:27
So what i'll do, we got to, i'm assuming we got to find the dimensions, how long should we make all the x lengths and how long should we make the y length? that's what i'm guessing.
01:41
So, well, to do that, i'll solve this for y.
01:45
I'm going to subtract the 4x.
01:49
So y equals 400 minus 4x.
01:55
So now i have something for y.
01:57
I can substitute that in.
01:59
So my area is going to be x times 4x...