Find the corner cutout size for maximum box volume

[Dustinsfl]

Consider a sheet of length L and width W.

Each corner is cut out (x by x corners removed).

Detemine the value of x so when the corners are removed and flaps folded up, the five sided box formed will have maximum volume.

SA \(= 1LW + 2 LH + 2WH\) and V \(= LWH\).

I am not sure how to do this maximizing problem.

 

[MarkFL]

See http://mathhelpboards.com/math-notes-49/folding-make-boxes-6366.html for a tutorial on this kind of problem. :D