00:01
Hi there, so for this problem we have an up and top, something like this, okay? then the dimensions for this are going to be x and x for the base because it has a square base and the height of this is y.
00:17
Then the materials for the sides cost five and the material for the base cost eight, right? and the volume for this should be equal to 100 cubic units, 100 cubic feet.
00:45
So then the volume is going to be x squared times y.
00:51
Once we have this, we can solve for y in here, so there will be 100 divided by x squared.
00:56
Once we have this, we know that the cost function is then equal to, well, the cost function is just the area for the specific size and the price for that.
01:06
Let's start with the base of this.
01:08
So the price for that is eight and the area for that is x squared.
01:17
Then for, we have four sides with an area of x times y and the price for that is five.
01:26
So simplifying the cost function in here, that will be then eight times x squared and this plus 20 times x times y.
01:43
And once we have, well, we can substitute in here y from the volume, so that will be 100 divided by x squared.
01:52
Simplifying this, there will be that the cost function is eight times x squared and this plus 2000 divided by x...