Multiple related variables... compromise... Sounds like a great
application for Excel's Solver feature.

For those of you who aren't familiar with it- its a brute force
computional method for optimization. Basically it allows you to tell
Excel to optimize (maximize, minimize, or seek value) for a particular
cell by manipulated a group of algebraicly related cell given a group
of contraints such "radius can't be a negative quantity". Pretty much
anything that might be a short optimization program in a high level
language is a candidate for Solver.