Physical Sciences and Mathematics Commons^™

An Extension Of The Fundamental Theorem Of Linear Programming, A Brown, A Gedlaman, Allen G. Holder, S Martinez

Mathematics Faculty Research

In 1947 George Dantzig developed the Simplex Algorithm for linear programming, and in doing so became known as The Father of Linear Programming. The invention of the Simplex Algorithm has been called "one of the most important discoveries of the 20th century," and linear programming techniques have proven useful in numerous fields of study. As such, topics in linear optimization are taught in a variety of disciplines. The finite convergence of the simplex algorithm hinges on a result stating that every linear program with an optimal solution has a basic optimal solution; a result known as the Fundamental Theorem of …