A version of the simplex method for solving linear systems of inequalities and linear programming problems

In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based on that function. Additional constraints can be used for accelerating calculations in the rst phase of the simplex method. As an example the solution of the Klee-Minty hypercube problem is described in detail.