| Preface | p. vii |
| Introduction | |
| General Discussion | p. 3 |
| Linear-Programming Problems | p. 3 |
| Examples of Linear-Programming Problems | p. 7 |
| Mathematical Background | p. 17 |
| Matrices | p. 17 |
| Vectors and Vector Spaces | p. 28 |
| Convex Sets | p. 32 |
| Linear Inequalities | p. 37 |
| Solution of a Set of Linear Equations | p. 43 |
| Methods: Theoretical and Computational | |
| The General Linear-Programming Problem | p. 67 |
| The Linear-Programming Problem | p. 67 |
| Properties of a Solution to the Linear-Programming Problem | p. 69 |
| Generating Extreme-Point Solutions | p. 77 |
| The Simplex Computational Procedure | p. 86 |
| Development of a Minimum Feasible Solution | p. 88 |
| Computational Procedure | p. 94 |
| The Artificial-Basis Technique | p. 106 |
| A First Feasible Solution Using Slack Variables | p. 113 |
| Geometric Interpretation of the Simplex Procedure | p. 114 |
| The Revised Simplex Method | p. 123 |
| The General Form of the Inverse | p. 123 |
| The Product Form of the Inverse | p. 139 |
| Computational Considerations | p. 142 |
| The Duality Problems of Linear Programming | p. 157 |
| The Unsymmetric Primal-Dual Problems | p. 157 |
| The Symmetric Primal-Dual Problems | p. 166 |
| Economic Interpretation of the Primal-Dual Problems | p. 173 |
| Degeneracy and Anticycling Procedures | p. 181 |
| Perturbation Techniques | p. 183 |
| The Lowest-Index Anticycling Rules | p. 186 |
| Example of Cycling | p. 190 |
| Parametric Linear Programming and Sensitivity Analysis | p. 195 |
| The Parametric Objective Function | p. 196 |
| The Parametric Dual Problem | p. 207 |
| Sensitivity Analysis | p. 213 |
| Multiobjective Linear Programming | p. 224 |
| Additional Computational Techniques | p. 238 |
| Determining a First Feasible Solution | p. 240 |
| The Dual Simplex Method | p. 245 |
| Integer Programming | p. 249 |
| The Decomposition of Large-Scale Systems | p. 266 |
| Bounded-Variable Problems | p. 282 |
| The Simplex Algorithm and Computational Efficiency | p. 303 |
| Applications | |
| The Transportation Problem | p. 319 |
| The General Transportation Problem | p. 319 |
| Computational Procedure for Solving the Transportation Problem | p. 328 |
| Variations of the Transportation Problem | p. 343 |
| General Linear-Programming Applications | p. 351 |
| Production-Scheduling and Inventory-Control Problems | p. 353 |
| Interindustry Problems | p. 362 |
| Diet Problems | p. 368 |
| Network-Flow Problems | p. 372 |
| Sample of Applications | p. 390 |
| Linear Programming and the Theory of Games | p. 406 |
| Nonlinear Programming | |
| Nonlinear Programming | p. 431 |
| The General Problem of Mathematical Programming | p. 432 |
| Mathematical Background | p. 435 |
| The Convex-Programming Problem | p. 442 |
| Quadratic Programming | p. 451 |
| Separable Programming | p. 458 |
| Bibliography of Linear-Programming Applications | p. 469 |
| References | p. 491 |
| Index | p. 525 |
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