00:01
A fence is to enclose an area of 5 ,000 square feet.
00:04
The material for the fence costs $4 per foot for the north and south sides and $8 per foot for the other two sides.
00:09
Find the cost of the least expensive fence.
00:11
So let's draw this fence here.
00:17
And we're going to let this length be x and this length be y.
00:24
So that means this would be x and this would be y.
00:27
We know that the fence area is to be 5 ,000 square feet.
00:31
So x times y needs to be 5 ,000 square feet.
00:36
So we also know that the costs will depend on how long x and y are.
00:45
So the cost of this side, of x side, we know it's going to be, that's the north and south side.
00:54
So that's $4 per foot.
00:56
So it's going to be $4 per however long x and x are.
01:02
So that would just be 2x.
01:04
And then plus the other sides are going to cost $8 per foot.
01:09
So that would be eight times y plus y or 2y.
01:13
So that gives us a cost of 8x plus 16y.
01:19
That's the function we want to minimize.
01:22
So we can solve this equation, x times y equals 5 ,000.
01:26
We could solve that for y.
01:29
So we know xy equals 5 ,000...