First, the

*2D* case is easy...

**Q0**: In a rectangle, we know that the sum of the dimensions (lenght and width) is a fixed $\displaystyle C$. Which are the dimensions values that maximize the area?

**A**: One dimension is $\displaystyle x$, and thus the other is $\displaystyle C-x$. Therefore, the area is $\displaystyle x \cdot (C-x) = xC - x^2$. Then, setting the derivative equal to zero would provide us the answer ($\displaystyle C/2$ on both dimensions)

Okay... now I want to generalize this to the

*3D* case. More precisely:

**Q1**: In a cuboid (see

en.wikipedia.org/wiki/Cuboid), we know that the sum of the dimensions (lenght, width and depth) is a fixed $\displaystyle C$. Which are the dimensions values that maximize the volume?

Finally, is there a generalization of the answer to Q1 for

*higher dimensions*?