The Simplex Method
In the graphical solution the optimum solution is always associated with a corner (or extreme) point of the solution space. The simplex method is based fundamentally on this idea. It employs an iterative process that starts at a feasible corner point normally the origin, and systematically moves from one feasible extreme point to another until the optimum point is eventually reached.
There are two rules that govern the choice of the next extreme point in the simplex method.
1) The next corner point must be adjacent to the current one.
2) The solution can never go back to a previously considered extreme point.