00:01
All right, hello, in this question we're told you want to build a fence along a house.
00:03
So i have my house over here.
00:06
I'll just say this is house.
00:09
I want to build a fence over here with dimensions x by y.
00:12
And i'm told that the area of this garden, the area of the fence region, is going to be 1050 feet squared.
00:19
I want to determine the dimensions that minimize the fencing material, providing this sketch.
00:26
So this would be my sketch.
00:28
I know my area is going to equal x times y, which equals 1050.
00:34
That's my constraint function.
00:35
So i'm going to go ahead and solve that for y, because i want to optimize the perimeter.
00:40
So my perimeter function, i'm going to have x plus 2y.
00:44
That's just the amount of fencing required for the three side.
00:47
They don't have to build a fence along the house.
00:49
And so i can go ahead and plug in my constraint function here.
00:53
So i'm going to have x plus 2100 over x.
00:59
And that will be my fence perimeter function.
01:02
I want to optimize that.
01:03
So i'm going to take a derivative.
01:04
I'll get 1 minus 2100 over x squared.
01:07
Set that equal to 0 and solve.
01:09
Well, x is going to be plus or minus the square root of 2100.
01:14
The minus doesn't make sense here, because this has to be a physical thing.
01:17
It has a length.
01:18
And so i don't want a negative length...