A simplified algebraic method for system of linear inequalities with LP applications

In this pedagogical note we present an improved method to solve and analyze linear programming (LP) problems. The method depends on solving a system of equations and is free of any slack, surplus or artificial variables. The proposed method eliminates the need to manipulate linear inequalities to introduce additional variables and works only within the original decision variables space. We present applications of the method to handle linear optimization with varying objective function. The proposed method is easy to implement and enhances understanding of the simplex method and LP solvers transparent. We believe it is a useful alternative approach to present LP in the class room during the first few hours of introducing the subject.