Elementary linear programming with applications / created by Bernard Kolman and Robert E Beck.

Includes bibliographical references and index.

Front Cover; Elementary Linear Programming with Applications; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; Prologue; Chapter 0. Review of Linear Algebra (Optional); 0.1 Matrices; 0.2 Gauss-Jordan Reduction; 0.3 The Inverse of a Matrix; 0.4 Subspaces; 0.5 Linear Independence and Basis; Further Reading; Chapter 1. Introduction to Linear Programming; 1.1 The Linear Programming Problem; 1.2 Matrix Notation; 1.3 Geometry of Linear Programming Problems; 1.4 The Extreme Point Theorem; 1.5 Basic Solutions; Further Reading; Chapter 2. The Simplex Method. 2.1 The Simplex Method for Problems in Standard Form2.2 Degeneracy and Cycling (Optional); 2.3 Artificial Variables; Further Reading; Chapter 3. Further Topics in Linear Programming; 3.1 Duality; 3.2 The Duality Theorem; 3.3 Computational Relations between the Primal and Dual Problems; 3.4 The Dual Simplex Method; 3.5 The Revised Simplex Method; 3.6 Sensitivity Analysis; 3.7 Computer Aspects (Optional); Further Reading; Chapter 4. Integer Programming; 4.1 Examples; 4.2 Cutting Plane Methods; 4.3 Branch and Bound Methods; 4.4 Computer Aspects (Optional); Further Reading. Chapter 5. Special Types of Linear Programming Problems5.1 The Transportation Problem; 5.2 The Assignment Problem; 5.3 Graphs and Networks: Basic Definitions; 5.4 The Maximal Flow Problem; 5.5 The Shortest Route Problem; 5.6 The Critical Path Method; 5.7 Computer Aspects (Optional); APPENDIX A: Karmarkar's Algorithm; APPENDIX B: Microcomputer Software; APPENDIX C: SMPX; Answers to Odd-Numbered Exercises; Index

Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications. The disk that comes with the book contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers. * More review material on linear algebra * Elementary linear programming covered more efficiently * Presentation improved, especially for the duality theorem, transportation problems, the assignment problem, and the maximal flow problem * New figures and exercises * Computer applications updated * Added disk with the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University * New guide to inexpensive linear programming software for personal computers.