Quantitative Analysis for Management
Topics: Optimization, Linear programming / Pages: 42 (10463 words) / Published: Mar 26th, 2012

Chapter 9

Learning Objectives
After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables 2. Set up and solve LP problems with simplex tableaus 3. Interpret the meaning of every number in a simplex tableau 4. Recognize special cases such as infeasibility, unboundedness, and degeneracy 5. Use the simplex tables to conduct sensitivity analysis 6. Construct the dual problem from the primal problem
© 2009 Prentice-Hall, Inc. 9–2

Linear Programming: The Simplex Method

© 2008 Prentice-Hall, Inc.

Chapter Outline
9.1 Introduction 9.2 How to Set Up the Initial Simplex Solution 9.3 Simplex Solution Procedures 9.4 The Second Simplex Tableau 9.5 Developing the Third Tableau 9.6 Review of Procedures for Solving LP Maximization Problems 9.7 Surplus and Artificial Variables 9.8 9.9 9.10 9.11 9.12 9.13

Chapter Outline
Solving Minimization Problems Review of Procedures for Solving LP Minimization Problems Special Cases Sensitivity Analysis with the Simplex Tableau The Dual Karmarkar’s Algorithm

© 2009 Prentice-Hall, Inc.

9–3

© 2009 Prentice-Hall, Inc.

9–4

Introduction
 With only two decision variables it is possible to

Introduction
 Why should we study the simplex method?  It is important to understand the ideas used to

use graphical methods to solve LP problems
 But most real life LP problems are too complex for  

 

simple graphical procedures We need a more powerful procedure called the simplex method The simplex method examines the corner points in a systematic fashion using basic algebraic concepts It does this in an iterative manner until an optimal solution is found Each iteration moves us closer to the optimal solution
© 2009 Prentice-Hall, Inc. 9–5

produce solutions
 It provides the optimal solution to the decision

variables and the maximum profit (or minimum cost)  It also provides important economic information  To be able

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