Equations which have requirements that represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).
Using linear programming someone is able to minimize the amount of debt being paid by setting equations and letting the program tell you the optimum path to paying it off. Equally as effective is using the programming to figure out how to maximize profit when deciding between various products with different prices and production costs.
An example would be myself, I used linear optimization to figure out how long and the best plan to minimize my current debt. The equations utilize current balance, interest rate, minimum payments, and any additional payments that can be made yearly or monthly.
Overall, if you know someone( possibly me :-| )who can assist you in doing this it is highly recommended, paying someone a small amount now could save you THOUSANDS or tens of thousands in the long run. There are agencies that can perform this task but I am sure they charge more than a component person and the results would be the same.