00:01
Hi there, so for this problem we suppose that an airline policy states that all baggage must be a box shaped with a sum of its length, width and height equals to 162.
00:20
So the question is what are the dimensions? so we need to determine the value of the length, the width and the height such that we will have the greatest volume.
00:31
We need to write a function for the volume of the box in terms of the width, one of the edges of the square bottom.
00:39
Now we are given some information for this.
00:45
We are told that this is a square based box so that means that the length is equal to the width and that's it.
00:55
So we can use this condition here and then we can write the volume of a box in this case is just the length, the width times the height.
01:12
If we substitute the condition that the length is equal to the width, we obtain in here the width squared times the height.
01:22
Now from this condition we can solve for the height.
01:27
So the height is 162 minus 2 times the width and then we can substitute that into the volume...