What optimisation method to use?

[makc]

for the problem:
- find H and W as functions of y0, E (having a method to solve for y0 = const, E=const is fine, too) such as product HW is max, under constraint: HW/(y0 + H) < E

if numeric, the method should be fast.

any suggestions?

 

[makc]

...from my attempt at solution, I have W < Ey0/H + E versus W = (max)/H, so it looks like for Ey0 <= 1 I have H approaching infinity, and for > 1 I have W approaching infinity.

can someone verify this?

...EDIT now when I think about it more, it seems because of "W < ... + E" increasing H is always favoured, maybe not if we limit W and H to something less then infinity (in real world they are values no more than ~1000).

 

[makc]

so it looks like this:

- if Ey0 > 1 compare results for max W versus max H under our constraint,
- otherwise use max H

am I right or what?