In order to implement this idea we need to specify some aspects:

  1. we have to represent vertices in algebraic form;
  2. how can we establish optimality and unboundness conditions;
  3. how can we move from one vertex of P to another, possibily better, one.
Finally, we have to be able to find an initial vertex of P or to prove that P is empty.
Let's now briefly overview how the simplex method performs these different aspects.