00:01
Hi there, so for this problem we are told that if the sum of its height and its breadth, it sits 108 inches.
00:12
So what we are given with that information is that the grid for this case is just 4 times x and then 4 times x plus the height for this case should be equal.
00:34
To 108, okay? so with that said, we need to opt to find the dimensions of x and the height that will maximize the volume of these spots, okay? then with that said, first of all, we consider that the volume for this box is equal to just simply x square times the height, okay? so now we're going to solve in here for the height, so the height is equal to 108 minus 4 times x and then substitute that into the volume.
01:11
So the volume now becomes x squared times 108 minus 4 times x.
01:19
Then let's expand this that will be 108 times x squared minus 4 times x to the 3.
01:27
Now since we want to maximize this function we derivated with respect to x and set that equal to 0.
01:35
So that will be 2 times 108, so that will give us 216 times x minus 12 times x squared.
01:47
And then we set this equal to 0.
01:50
Then we will have 216 is equal to 12 times adds...