00:01
All right, so in this problem, we have a rancher.
00:02
He only has 400 feet of fencing, and he wants to make a rectangular corral, and it's going to be divided into three equal parts or three pieces inside.
00:12
So, this is a barn.
00:15
Let's get a picture of what this looks like.
00:19
So here's a barn.
00:22
So he's going to have one piece of fencing out here.
00:30
He's going to have a fence at the end, a fence at this end.
00:35
And then you're going to have two other pieces of fencing in the middle somewhere in order to maximize or in order to have the three little sections inside.
00:45
Okay, there's no fencing for the barn.
00:49
So if we call all of those vertical pieces y and then we call this horizontal piece x, we know that the x plus the four y's is going to equal 400 because that's all the fencing that this rancher has 400 feet.
01:21
Okay, we want to maximize the area.
01:25
We want to maximize the area.
01:28
Okay, well, let's find the format for area.
01:31
So the area is just going to be the x times the y.
01:41
But we don't want, you know, having the area equal to, having the area equal to x and y is a problem.
01:51
We want it equal to just one variable.
01:54
Probably the easiest thing to do is just solve for x.
02:00
So if i subtract 4y from both sides, x is going to equal 400 minus 4y.
02:11
So now my area formula i could substitute in for x, and so my area with respect to just a y value is going to be the 400 minus 4y.
02:25
Times y.
02:28
Okay, awesome...