Date of Award

Spring 1959

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Talacko, Joseph V.

Second Advisor

Hanneken, C.B.

Third Advisor

Pettit, Harvey

Abstract

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' 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.

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