Linear Programming Lecture Notes

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Linear Programming : Penn State Math 484Lecture NotesVersion Griffin 2009-2014Licensed under a Creative Commons Attribution-Noncommercial-Share Alike United States LicenseWith Contributions By:Bob Pakzad-HursonGreg FerenceVeselka KafedzhievaMichael ClineAkinwale AkinbiyiEthan WrightRichard BenjaminDouglas MercerContentsList of FiguresvPrefaceixChapter 1. Introduction to Optimization11. A General Maximization Formulation22. Some Geometry for Optimization43. Gradients, Constraints and Optimization10Chapter 2. Simple Linear Programming Problems131. Modeling Assumptions in Linear Programming142. Graphically Solving Linear Programs Problems with Two Variables (BoundedCase)163. Formalizing The Graphical Method174. Problems with Alternative Optimal Solutions185. Problems with No Solution206. Problems with Unbounded Feasible Regions22Chapter 3.

has two extreme points (0;1) and (1=2;1=2).64 4.11 The Cartheodory Characterization Theorem: Extreme points and extreme directions are used to express points in a bounded and unbounded set.68 5.1 The Simplex Algorithm: The path around the feasible region is shown in the gure. Each exchange of a basic and non-basic variable moves us along an edge

  Characterization