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

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