An Approach to the General Solution of Linear Programming Problems

The general linear programming problem is one of optimizing a linear functional of several variables subject to a set of linear inequalities which restrict domain. Problems of this sort are of immence practical importance, and yet, until not so long ago, many thought no more exact or general method of\u27 solution than trial and error was possible. In 1950, however, G. B. Dantzig discovered an itarative procedure called the Simplex Method which finds the exact solution in a finite number of steps in most cases. Unfortunately, the Simplex Method, as well as more recent techniques, is based on the theory of linear equations rather than inequalities. This not only introduces computational complications, such as that of first converting the problems inequalities into equations by addition of artificial slack variables, but also tends to obscure the beauty and simplicity of the theory. In this paper, therefore, the object is to devise a theoretical technique for the solution of the general linear programming problem which is based directly on the properties of linear inequalities