Elementary Linear Programming with Applications

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.
- 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
- New guide to inexpensive linear programming software for personal computers

Prologue: Introduction to Operations Research. Review of Linear Algebra: Matrices. Gauss-Jordan Reduction. The Inverse of a Matrix. Subspaces. Linear Independence and Basis. Introduction to Linear Programming: The Linear Programming Problem. Matrix Notation. Geometry of Linear Programming Problems. The Extreme Point Theorem. Basic Solutions. The Simplex Method: The Simplex Method for Problems in Standard Form. Degeneracy and Cycling. Artificial Variables.Further Topics in Linear Programming: Duality. The Duality Theorem. Computational Relations between the Primal and Dual Problems. The Dual Simplex Method. The Revised Simplex Method. Sensitivity Analysis. Computer Aspects. Integer Programming: Examples. Cutting Plane Methods. Branch and Bound Methods. Computer Aspects. Special Types of Linear Programming Problems: The Transportation Problem. The Assignment Problem. Graphs and Networks (Basic Definitions). The Maximal Flow Problem. The Shortest Route Problem. The Critical Path Method. Computer Aspects. Appendices: Karmarkar's Algorithm. Microcomputer Software. SMPX. Answers to Odd-Numbered Exercises. Index.