00:01
Hi there, so for this problem we have that the baggage, okay, so let me just try in here some box in here.
00:09
Now let's label the length, the width and the height of this and then we're told that for this box shape it with a sum of the length, we're told that the length plus the width plus the height should be not exceeding 64 inches.
00:28
So this should be equal to 64, right? now the question is what are the dimensions? so we need to determine the length, the width and the height and the volume of an square base box with the greatest volume.
00:41
Now, since it is a square base box, then the length equals to the width.
00:48
So with that, the previous expression simplifies, we are going to then substitute the length for the width.
00:54
So that will give us two times the width plus the height equals to 64.
00:58
For example, if we want to solve for the height, that will give us 64 minus two times the width.
01:04
Now we need to maximize the volume for this.
01:07
Now the volume, remember that is the length, the width times the height.
01:10
If we substitute the condition that the length is equal to the width, that will give us the width of square times the height.
01:16
Now we need to maximize this equation.
01:18
So we are going to substitute in here the expression that we obtained from before for the condition that we are given.
01:23
So that for the height, so that will be the width of square times 64 minus two times the width.
01:30
And now let's expand this in here...