The Non-Substitution Theorem and Uniqueness of Solution in Linear Programming

Our first result is a statement of a somewhat general form of a non-substitution theorem for linear programming problems, along with a very easy proof of the same. Subsequently, we provide an easy proof of theorem 1 in Mangasarian (1979), based on a lemma that may be of some significance by itself. As a result of our lemma, we are able to show that a necessary and sufficient condition for a solution for a linear programming problem to be its unique solution, is that a system of linear inequalities has a solution whose last coordinate is non-negative.