Linear Programming and Its Applications (Paperback, Softcover Repri)

0 Introduction.- I: Linear Programming.- 1 Geometric Linear Programming.- 0. Introduction.- 1. Two Examples: Profit Maximization and Cost Minimization.- 2. Canonical Forms for Linear Programming Problems.- 3. Polyhedral Convex Sets.- 4. The Two Examples Revisited.- 5. A Geometric Method for Linear Programming.- 6. Concluding Remarks.- Exercises.- 2 The Simplex Algorithm.- 0. Introduction.- 1. Canonical Slack Forms for Linear Programming Problems; Tucker Tableaus.- 2. An Example: Profit Maximization.- 3. The Pivot Transformation.- 4. An Example: Cost Minimization.- 5. The Simplex Algorithm for Maximum Basic Feasible Tableaus.- 6. The Simplex Algorithm for Maximum Tableaus.- 7. Negative Transposition; The Simplex Algorithm for Minimum Tableaus.- 8. Cycling.- 9. Concluding Remarks.- Exercises.- 3 Noncanonical Linear Programming Problems.- 0. Introduction.- 1. Unconstrained Variables.- 2. Equations of Constraint.- 3. Concluding Remarks.- Exercises.- 4 Duality Theory.- 0. Introduction.- 1. Duality in Canonical Tableaus.- 2. The Dual Simplex Algorithm.- 3. Matrix Formulation of Canonical Tableaus.- 4. The Duality Equation.- 5. The Duality Theorem.- 6. Duality in Noncanonical Tableaus.- 7. Concluding Remarks.- Exercises.- II: Applications.- 5 Matrix Games.- 0. Introduction.- 1. An Example; Two-Person Zero-Sum Matrix Games.- 2. Linear Programming Formulation of Matrix Games.- 3. The Von Neumann Minimax Theorem.- 4. The Example Revisited.- 5. Two More Examples.- 6. Concluding Remarks.- Exercises.- 6 Transportation and Assignment Problems.- 0. Introduction.- 1. An Example; The Balanced Transportation Problem.- 2. The Vogel Advanced-Start Method (VAM).- 3. The Transportation Algorithm.- 4. Another Example.- 5. Unbalanced Transportation Problems.- 6. The Assignment Problem.- 7. Concluding Remarks.- Exercises.- 7 Network-Flow Problems.- 0. Introduction.- 1. Graph-Theoretic Preliminaries.- 2. The Maximal-Flow Network Problem.- 3. The Max-Flow Min-Cut Theorem; The Maximal-Flow Algorithm.- 4. The Shortest-Path Network Problem.- 5. The Minimal-Cost-Flow Network Problem.- 6. Transportation and Assignment Problems Revisited.- 7. Concluding Remarks.- Exercises.- APPENDIX A Matrix Algebra.- APPENDIX B Probability.- Answers to Selected Exercises.