## Introduction to Linear Programming: Applications and ExtensionsStressing the use of several software packages based on simplex method variations, this text teaches linear programming's four phases through actual practice. It shows how to decide whether LP models should be applied, set up appropriate models, use software to solve them, and examine solutions to a |

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### Contents

Introduction to Systems of Linear Equations Linear | 1 |

Introduction to Linear Programming | 24 |

Elementary Properties of the Feasible Set for an LP | 64 |

Introduction to the Simplex Method | 80 |

Topics in LP and Extensions | 114 |

Duality | 202 |

Quadratic Programming | 208 |

Minimizing a Quadratic Function | 226 |

Network Algorithms | 246 |

Forms of LPs | 273 |

Solutions Supplement for Chapter 2 | 278 |

Solutions Supplement for Chapter 5 | 315 |

346 | |

### Common terms and phrases

0-1 integer variables algebra apply appropriate LP augmented augmented matrix basic feasible solution Chapter column vector companion mix compute consider constraints convex corner points corresponding cycle decision variables denote discussed dynamic programming equal to zero equations ex s.t. Example 2.1 feasible set following LP Formulate an appropriate Formulate an LP fuel oil graph jet fuel kilograms Kuhn-Tucker conditions linear program linear system linearly independent LP model machine matrix maximize maximum flow maximum flow problem minimal minimum value NOcycle node OBJECTIVE FUNCTION VALUE optimal BFS optimal solution primal-dual pair produce Q is positive quadratic function quadratic program residual digraph route row reduction scanned Section simplex method slack variables solution to Exercise solve standard-form LP steepest descent SUBJECT Suppose surplus variables symmetric primal tableau theorem topologically ordered transportation problem truckloads unit VALUE REDUCED COST VARIABLE VALUE REDUCED x'Qx