Linear Programming (LP) and Integer Linear Programming (ILP) are two of the most powerful tools ever created in mathematics. Their usefulness comes from the many areas where they can provide satisfactory modeling and solving techniques to real-life problems. Their appeal comes from the rich combinatorial and geometric theory they are based upon. Solving an LP problem consists in minimizing a linear functional over a polyhedron, which, in turn, amounts to detecting a vertex of the polyhedron where the linear functional achieves the minimum (if it exists).
