00:01
In this problem, we have this rectangular box with a square base.
00:07
So something like this.
00:12
Let's call this size a, a and b.
00:16
We know that the volume is equal to 5200 cubic inches.
00:26
And we require the length of the base and the height to be less than 48 inches.
00:34
Now we want to construct this box and we want to use double layers at the base and at the top.
00:48
So double layer here and double layers here.
00:57
So the question is what are the dimensions of the box that will minimize the amount of carpet that is going to be used.
01:07
Let's write down the surface function.
01:11
We have 2a squared here, 2a squared here because they are double layered.
01:18
So 4a squared plus 4 times ab.
01:23
Using the fact that volume is equal to a squared b, we have b equal to 5200 over a squared...