Chvatal V. Linear Programming

W.H. Freeman, 1983. - 485 pages.

This book include some background in linear algebra and some experience with proof based mathematics. It makes a good subject for students to study as they are developing proof writing skills.
The first 10 chapters of the book present the simplex method, the revised simplex method, duality theory, and sensitivity analysis.
The remaining chapters of the book are largely independent, mostly focused on various applications of linear programming and specialization of the simplex method to network flow problems.

Contents
Preface
Basic Theory
Introduction
How the Simplex Method Works
Pitfalls and How to Avoid Them
How Fast Is the Simplex Method?
The Duality Theorem
Gaussian Elimination and Matrices
The Revised Simplex Method
General LP Problems: Solutions by the Simplex Method
General LP Problems: Theorems on Duality and Infeasibility
Sensitivity Analysis

Selected Applications
Efficient Allocation of Scarce Resources
Scheduling Production and Inventory
The Cutting-Stock Problem
Approximating Data by Linear Functions
Matrix Games
Systems of Linear Inequalities
Connections with Geometry
Finding All Vertices of a Polyhedron

Network Flow Problems
The Network Simplex Method
Applications of the Network Simplex Method
Upper-Bounded Transshipment Problems
Maximum Flows Through Networks
The Primal-Dual Method

Advanced Techniques
Updating a Triangular Factorization of the Basis
Generalized Upper Bounding
The Dantzig-Wolfe Decomposition Principle

Index: The Ellipsoid Method
Bibliography