The integrated software supporting the execution of interactive
examples "re-uses" the very nice software modules developed by (i)
**Drs Ken Goldberg** and **Ilan Adler** at
the **Dept. of Industrial Engineering and Operations
Research**, **University of California at
Berkeley**, and (ii) **Dr. Timothy Wisniewski**,
of **Northwestern University**. The remaining JAVA
applets were developed "in house", by ** Panagiotis
Reveliotis**. In fact, this software is still under testing, so,
please, report any problems with it, to *spyros@isye.gatech.edu*.

This text is intended to
function as an introduction to *Linear Programming (LP)* and
the *Simplex algorithm*. The specific topics covered and the
structure of the material is as follows:

- The LP formulation and the underlying assumptions
- Graphical solution of 2-var LP's
- Generalization to the
*n*-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear Programming. - An algebraic characterization of the solution search space: Basic Feasible Solutions
- The Simplex Algorithm

Most of the text material is presented inductively, by
generalizing some introductory highlighting examples. In fact, the
basic structure of the material and many of the examples used in the
text have been inspired by W. L. Winston's *``Introduction to
Mathematical Programming''*, ed. Duxbury, which has been used as
the class text in an introductory LP course at the School of
Industrial & Systems Engineering, at Georgia Tech.

An additional and innovative feature of this text is the integration of some software modules which allow the reader to run her own examples interactively. Specifically, this software is distributed at the end of key sections, and it is intended to demonstrate/visualize basic concepts and the functionality of the algorithms discussed in the text.

- The LP formulation and the underlying assumptions
- Graphical solution of
2-var LP's
- Feasible Regions of Two-Var LP's
- The solution space of a single equality constraint
- The solution space of a single inequality constraint
- Representing the Objective Function in the LP solution space
- Graphical solution of the prototype example: a 2-var LP with a unique optimal solution
- 2-var LP's with many optimal solutions
- Infeasible 2-var LP's
- Unbounded 2-var LP's

- Generalization to the
*n*-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear Programming - An algebraic characterization of the solution search space: Basic Feasible Solutions
- The Simplex Algorithm
- About this document ...

Fri Jun 20 15:03:05 CDT 1997