Visualization of Dual Feasible Bases in Primal Space

HINE ZAHEER; MUHAMMAD IMTIYAZ; HAFSA ATHAR JAFREE

HINE ZAHEER Department of Mathematics, University of Karachi, Karachi
MUHAMMAD IMTIYAZ Department of Mathematics, University of Karachi, Karachi
HAFSA ATHAR JAFREE Department of Mathematics, University of Karachi, Karachi

Keywords: Linear programming, Graphical Method, Farkas', Lemma, Karush-Kuhn-Tucker Conditions

Abstract

In this article, we have presented a new variant of Karush-Kuhn-Tucker (KKT) conditions and a simplified proof of KKT conditions has also been given to illustrate the association of both primal and dual solutions in a primal space. Furthermore, taking the aid of KKT conditions an extension of graphical method for solving two (may be extended to three by help of computer graphical softwares) dimensional LPs has been presented which can incorporate both primal and dual feasible solutions of an LP simultaneously in a single graph. A numerical example has also been given to demonstrate the proposed approach. This article will assist in providing students a better insight of the geometry of weak and strong duality theorem for primal and dual pairs of LPs.