I'm trying to optimize the volume of a computer by maximizing for volume while keeping my surface area at a constant. The allowed surface are ais 2783.78 cm^2 The second constraint is that the length and height must always be greater than or equal to 24.4 cm; the computer must be able to fit a motherboard (24.4x24.4cm). That makes constaint 1: 2lw+2hw+2lh=2783.78 And constraint 2: l≥24.4, h≥24.4
Does anyone know any methods of optimmizing this? I've heard of lagrange multipliers. but I'd like different approaches Right now, I was thinking of utilizing an 'iterative'/'algorithmic' approach; wherein I'd just trial and error different h/w/l values and see which gives a high volume. I want to then use a second, more accurate approach. and then my third method would be lagrange multipliers which would give me the largest, most accurate volume possible.
Thanks