00:01
Okay, so we have a closed box.
00:03
We know that the volume, okay, so we've given this box, we know that the top costs 10 cents per square foot, the bottom is 20 cents per square foot, and the sides are 2 cents per square foot.
00:22
We want to minimize the cost.
00:24
Okay, so the first term, this is the bottom.
00:35
This one's the top.
00:37
And then this is the two cents per side.
00:43
So we got two of each side times two cents apiece.
00:47
So that's where that comes from.
00:49
So our cost function looks like this.
00:59
All right.
01:00
We want to minimize the cost.
01:02
So our objective function is going to look like this.
01:05
We get one lagrange multiplier because we have one constraint which is the constraint on the volume.
01:29
Okay and then we take some derivatives and then we set them all equal to zero and then we number them.
02:43
We'll come down here and i'm going to take equation 3 i'm going to solve it for lambda.
03:06
All right.
03:08
I'm going to do the same thing with equation 2.
03:14
Okay.
03:15
And then let's subtract those first two equations...