## An Introduction to Linear Programming and the Theory of GamesSimple exposition of linear programming and matrix games covers convex sets in the Cartesian plane and the fundamental extreme point theorem for convex polygons; the simplex method in linear programming; the fundamental duality theorem and its corollary, von Neumann's minimax theorem; more. Easily understood problems and illustrative exercises. 1963 edition. |

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### Contents

Elementary Aspects of Linear Programming | 1 |

Alternate Optimal Solutions | 13 |

Convex Sets in the Cartesian Plane and | 22 |

Convex Sets in the Cartesian Plane | 29 |

Convex Subsets of a Line | 38 |

The Fundamental Extreme Point Theorem | 49 |

The Simplex Method in Linear Programming | 58 |

The Use of Artificial Variables | 70 |

The Condensed Simplex Tableau | 74 |

Graphical Analysis ofmy 2 and 2 x n Matrix Games | 97 |

Matrix Games and Linear Programming | 111 |

127 | |

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### Common terms and phrases

A's optimal strategy algebraic analysis artificial variables basic feasible solution basic variables basis Bibliography boundary point Bulkswagons called cartesian plane choose Classic closed half plane closed segment codeine Condensed Tableau constraints convex polygon corresponding defined DEFINITION Determine DIFFERENTIAL EQUATIONS dual edge elementary endpoint example Exercises expected payoff extreme point Figure finite number function Game Theory geometry grains of aspirin half line inequalities interior point INTRODUCTION iteration last row linear form linear programming linear programming problems matching pennies mathematical matrix game Minimax Theorem minimum value minutes mixed strategy nonbasic obtain optimal solution optimal tableau ordered pairs parameter value parametric representation payoff matrix plays HEADS plays TAILS points of JT polygonal convex region polygonal convex set Pontillacs proof Prove pure strategy real numbers saddle point set of points Simplex Method slack variables solution set solve strategy point Theory of Games topology upper bound values assumed vertices x 8K yields zero