You folks may want to acquaint yourselves with linear programming, if you haven't heard about it before:
a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).
Linear programming - Wikipedia
I have also worked with non-linear programming (actually quadratic programming), which deals with more complex relationships:
Nonlinear programming - Wikipedia
- xongsmith, 5.7d