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| Preface | |
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| Mathematical Models | |
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| Applying Mathematics | |
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| The Diet Problem | |
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| The Prisoner's Dilemma | |
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| The Roles of Linear Programming and Game Theory | |
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| The Linear Programming Model | |
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| History | |
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| The Blending Model | |
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| The Production Model | |
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| The Transportation Model | |
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| The Dynamic Planning Model | |
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| Summary | |
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| The Simplex Method | |
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| The General Problem | |
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| Linear Equations and Basic Feasible Solutions | |
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| Introduction to the Simplex Method | |
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| Theory of the Simplex Method | |
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| The Simplex Tableau and Examples | |
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| Artificial Variables | |
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| Redundant Systems | |
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| A Convergence Proof | |
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| Linear Programming and Convexity | |
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| Spreadsheet Solution of a Linear Programming Problem | |
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| Duality | |
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| Introduction to Duality | |
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| Definition of the Dual Problem | |
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| Examples and Interpretations | |
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| The Duality Theorem | |
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| The Complementary Slackness Theorem | |
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| Sensitivity Analysis | |
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| Examples in Sensitivity Analysis | |
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| Matrix Representation of the Simplex Algorithm | |
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| Changes in the Objective Function | |
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| Addition of a New Variable | |
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| Changes in the Constant-Term Column Vector | |
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| The Dual Simplex Algorithm | |
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| Addition of a Constraint | |
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| Integer Programming | |
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| Introduction to Integer Programming | |
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| Models with Integer Programming Formulations | |
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| Gomory's Cutting Plane Algorithm | |
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| A Branch and Bound Algorithm | |
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| Spreadsheet Solution of an Integer Programming Problem | |
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| The Transportation Problem | |
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| A Distribution Problem | |
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| The Transportation Problem | |
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| Applications | |
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| Other Topics in Linear Programming | |
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| An Example Involving Uncertainty | |
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| An Example with Multiple Goals | |
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| An Example Using Decomposition | |
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| An Example in Data Envelopment Analysis | |
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| Two-Person, Zero-Sum Games | |
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| Introduction to Game Theory | |
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| Some Principles of Decision Making in Game Theory | |
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| Saddle Points | |
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| Mixed Strategies | |
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| The Fundamental Theorem | |
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| Computational Techniques | |
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| Games People Play | |
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| Other Topics in Game Theory | |
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| Utility Theory | |
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| Two-Person, Non-Zero-Sum Games | |
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| Noncooperative Two-Person Games | |
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| Cooperative Two-Person Games | |
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| The Axioms of Nash | |
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| An Example | |
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| Vectors and Matrices | |
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| An Example of Cycling | |
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| Efficiency of the Simplex Method | |
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| LP Assistant | |
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| Microsoft Excel and Solver | |
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| Bibliography | |
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| Solutions to Selected Problems | |
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| Index | |