Sorry, I didn't even know bbcode supported that.
Here we go.
We know that the area is equal to 2400. However the equation for that amount is still very necessary. To find area of one side we like to use

, where

= Length and

= Width. In order to find the area of a Rectangular box we need to add up the area of each side.
For this we are going to add another variable in order to show where sides are the same measure, and because it is three dimensional we will use

for height.
If you look at the image you will notice that each of box's faces have one opposite of them that is exactly the same size. Normally that would give us the following equation for the area:
Even though the left goes into infinity, it doesn't matter because X
Width cannot be negative and even though it goes to negative infinity to the right it does not matter because Y
Volume cannot be negative either.
The maximum is going to be between the two x intercepts.

.
The fact that the ends are square helps us out a lot. That means that

. This means we can substitute

for

, which would result in the following equation:
Simplified:
Our next important equation is that for volume

where

,

, and

are the same and

is volume.
Once again

is the same as

and can be supplemented in, resulting in:
Simplified:
Using the equation for area we could never find maximum volume because it doesn't even have volume in it. The volume equation we just made couldn't find it because it is dependent on the unknown

and

, meaning there are infinite possibilities.
So to achieve the question, we limit the volume equation by the area equation. This is kind of like saying the volume equation depends on the results of the area equation. This is done by putting the volume equation inside of the area equation. I'll show you how.
Solve

for

:
Remember: What ever you do to one side of the equation you must do to the other.
Simplified:
Now we have an equation for

that we can substitute into the area equation.
Hint: By doing this, we have placed the volume equation inside of the area equation.
Simplified1:
Simplified2:
The next thing to do is find volume:
First we need to have volume on one side of the equation in order to solve for it.
Hint: A number times its inverse is always 1
Each part divided by

:
If we graphed that it would look something like:
Note: The numbers are not correct.