challenge: dynamic formulas?

[nanode]

I don't have a formal mathematics background so bare with me if my terminology is off.

I'd like to make a small app. that determines all the possible values that a formula can take as args to produce a known result.

An over simplified example would be calculating volume of an aquarium. volume = length * width * height

Suppose I needed a given volume (say 1000cm3) and a given width (say 50cm) and wanted to find out all the combinations of height and length (of integers) that would result in my desired volume?

Other than incrementing in a loop from 0 to n for each unspecified parameter, is there a way (elegantly) to solve this?

I suck at math - thanks in advance. :)

[Stuka]

nanode-
Unfortunately, the general solution to this is a fairly complex mathematical arrangement. In general, to find the max/min values of a function f(x,y,z) subject to some constraint g(x,y,z), you solve a system of equations formed by: gradient(f(x,y,z)) = k*gradient(g(x,y,z)), where k is an undetermined constant. This gives you 4 equations in the 4 unknowns (x,y,z, and k). Then solve those equations to get the numbers giving max/min values.

[Strike]

yup, what Stuka is talking about is known as Lagrange multipliers. You can probably do some research on this and maybe find a simplified solution.

[Stuka]

I can't believe it...all that spewin' and I didn't even have the decency to tell him the name! :(

[nanode]

Thanks for the replies. Doesn't sound as simple as I'd hoped, but at least there is a name for it, so I can research a bit.