## An Introduction to Linear Programming and Game TheoryA rigorous introduction to the theoretical concepts and computational techniques of linear programming and game theory. Illustrates how mathematics can be used to understand and resolve real world problems. Standard topics are covered--the simplex algorithm; duality; sensitivity; integer programming; the transportation problem; two-person, zero-sum, and non-zero sum games--and in the process, mathematical model-building is explained. Material includes meaningful examples and numerous exercises to reinforce and enhance understanding. Examples are used extensively, and the exercises (over 500) range in nature from model building and computation to theory. In this edition five new sections have been added, new problems included, and material expanded and improved. |

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### Contents

MATHEMATICAL MODELS l | 1 |

THE LINEAR PROGRAMMING MODEL | 9 |

THE SIMPLEX METHOD | 45 |

Copyright | |

10 other sections not shown

### Other editions - View all

An Introduction to Linear Programming and Game Theory Paul R. Thie,Gerard E. Keough Limited preview - 2011 |

### Common terms and phrases

aluminum amount artificial variables assignment attained basic feasible solution basic variables branch and bound canonical form coefficients column Compute constant terms convex set corresponding defined demands denote destinations determine diet distribution problem dual problem Dual Simplex Algorithm entries equal equilibrium equivalent final tableau form with basic game theory inequalities integer programming labor linear programming problem man-hours mathematical model matrix game Maximize maximum minimal cost minimal value minimum mixed strategy nonbasic variables nonnegative number of units objective function optimal production schedule optimal solution point optimal strategy optimal value original problem outcome payoff matrix pivot operation pivot term Plant play players problem of Minimizing PROBLEM SET profit proof pure strategies raw materials requirements saddle point Section 5.1 security level simplex method slack variables Solve step strategy pair Suppose system of constraints system of equations tableau of Table transportation problem algorithm two-person vector zero zero-sum games