  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.
