QA index

A

Analysisement

GLOBAL EDITIONELEVENTH EDITION

Charles Harwood Professor of Management ScienceGraduate School of Business, Rollins College

Professor of Information and Management Sciences,Florida State University

Professor of Decision Sciences,University of Houston—Clear Lake

Boston Columbus Indianapolis New York San Francisco Upper Saddle RiverAmsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto

Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

CONTENTS

PREFACE 15

CHAPTER 1 Introduction to QuantitativeAnalysis 21

1.1 Introduction 22

1.2 What Is Quantitative Analysis? 22

1.3 The Quantitative Analysis Approach 23

Defining the Problem 23

Developing a Model 23

Acquiring Input Data 24

Developing a Solution 25

Testing the Solution 25

Analyzing the Results and Sensitivity Analysis 25

Implementing the Results 25

The Quantitative Analysis Approach andModeling in the Real World 27

1.4 How to Develop a Quantitative AnalysisModel 27 ,

The Advantages of Mathematical Modeling 28

Mathematical Models Categorized by Risk 28

1.5 The Role of Computers and Spreadsheet Modelsin the Quantitative Analysis Approach 29

1.6 Possible Problems in the Quantitative AnalysisApproach 32

Defining the Problem 32

Developing a Model 33

Acquiring Input Data 33

Developing a Solution 34

Testing the Solution 34

Analyzing the Results 34

1.7 Implementation—Not Just the Final Step 35

Lack of Commitment and Resistance to Change 35

Lack of Commitment by Quantitative Analysts 35

Summary 36 Glossary 36 Key Equations 36Self-Test 37 Discussion Questions and Problems37 Case Study: Food and Beverages at SouthwesternUniversity Football Games 39 Bibliography 39

CHAPTER 2 Probability Concepts and Applications 412.1 Introduction 42

2.2 Fundamental Concepts 42

Types of Probability 43

2.3 Mutually Exclusive and CollectivelyExhaustive Events 44

Adding Mutually Exclusive Events 46

Law of Addition for Events That Are NotMutually Exclusive 46

2.4 Statistically Independent Events 47

2.5 Statistically Dependent Events 48

2.6 Revising Probabilities with Bayes'Theorem 49General Form of Bayes' Theorem 51

2.7 Further Probability Revisions 52

2.8 Random Variables 53

2.9 Probability Distributions 54Probability Distribution of a Discrete Random

Variable 54Expected Value of a Discrete Probability

Distribution 55

Variance of a Discrete Probability Distribution 56Probability Distribution of a Continuous

Random Variable 562.10 The Binomial Distribution 58

Solving Problems with the Binomial Formula 59

Solving Problems with Binomial Tables 60

2.11 The Normal Distribution 61

Area Under the Normal Curve 62

Using the Standard Normal Table 62 s

Haynes Construction Company Example 64

The Empirical Rule 68

2.12 The F Distribution 68

2.13 The Exponential Distribution 70

Arnold's Muffler Example 71

2.14 The Poisson Distribution 72

Summary 74 Glossary 74 Key Equations 75Solved Problems 76 Self-Test 79 DiscussionQuestions and Problems 80 Case Study:WTVX 85 Bibliography 86

Appendix 2.1 Derivation of Bayes' Theoreni 86

Appendix 2.2 Basic Statistics Using Excel 86

CIWTIIR3 Decision Analysis 893.1 Introduction 903.2 The Six Steps in Decision Making 903.3 Types of Decision-Making Environments 913.4 Decision Making Under Uncertainty 92

Optimistic 92Pessimistic 93Criterion of Realism (Hurwicz Criterion) 93

CONTENTS

Equally Likely (Laplace) 94

Minimax Regret 94

3.5 Decision Making Under Risk 96Expected Monetary Value 96

Expected Value of Perfect Information 97

Expected Opportunity Loss 98

Sensitivity Analysis 99

Using Excel QM to Solve Decision TheoryProblems 100

3.6 Decision Trees 101

Efficiency of Sample Information 106

Sensitivity Analysis 106

3.7 How Probability Values are Estimated byBayesian Analysis 107

Calculating Revised Probabilities 107

Potential Problem in Using Survey Results 109

3.8 Utility Theory 110

Measuring Utility and Constructing a UtilityCurve 111

Utility as a Decision-Making Criterion 113

Summary 115 Glossary 115 Key Equations 116Solved Problems 117 Self-Test 122 DiscussionQuestions and Problems 123 Case Study:Starting Right Corporation 130 Case Study:Blake Electronics 131 Bibliography 133

Appendix 3.1 Decision Models with QM for Windows 133Appendix 3.2 Decision Trees with QMfor Windows 134

Regression Models 1354.1 Introduction 136

4.2 Scatter Diagrams 136

4.3 Simple Linear Regression 137

4.4 Measuring the Fit of the Regression Model 139

Coefficient of Determination 140

Correlation Coefficient 141

4.5 Using Computer Software for Regression 142

4.6 Assumptions of the Regression Model 143

Estimating the Variance 145

4.7 Testing the Model for Significance 145

Triple A Construction Example 147

The Analysis of Variance (ANOVA) Table 147

Triple A Construction ANOVA Example 148

4.8 Multiple Regression Analysis 148

Evaluating the Multiple Regression Model 149

Jenny Wilson Realty Example 150

4.9 Binary or Dummy Variables 151

4.10 Model Building 152 •

4.11 Nonlinear Regression 153

4.12 Cautions and Pitfalls in RegressionAnalysis 156

Summary 156 Glossary 157 Key Equations 157Solved Problems 158 Self-Test 160 DiscussionQuestions and Problems 160 Case Study:North-South Airline 165 Bibliography 166

Appendix 4.1 Formulas for Regression Calculations 166

Appendix 4.2 Regression Models Using QMforWindows 168

Appendix 4.3 Regression Analysis in Excel QM orExcel 2007 170

CHAPTER 5 Forecasting 173

5.1 Introduction 174

5.2 Types of Forecasts 174

Time-Series Models 174

Causal Models 174

Qualitative Models 175

5.3 Scatter Diagrams and Time Series 176

5.4 Measures of Forecast Accuracy 178

5.5 Time-Series Forecasting Models 180

Components of a Time Series 180

Moving Averages 181

Exponential Smoothing 184

Using Excel QM for Trend-Adjusted ExponentialSmoothing 189

Trend Projections' 189

Seasonal Variations 191

Seasonal Variations with Trend 193

The Decomposition Method of Forecasting withTrend and Seasonal Components 195

Using Regression with Trend and SeasonalComponents 197

5.6 Monitoring and Controlling Forecasts 199

Adaptive Smoothing 201

Summary 201 Glossary 202 Key Equations 202Solved Problems 203 Self-Test 204 DiscussionQuestions and Problems 205 Case Study:Forecasting Attendance at SWU FootballGames 209

Case Study: Forecasting Monthly Sales 210

Bibliography 211

Appendix 5.1

CHAPITER 66.16.2

6.36.4

6.5

Forecasting with QMfor Windows 211

Inventory Control Models 215Introduction 216Importance of Inventory Control 216Decoupling Function 217

Storing Resources 217

Irregular Supply and Demand 217

Quantity Discounts 217

Avoiding Stockouts and Shortages 217

Inventory Decisions 217Economic Order Quantity: Determining HowMuch to Order 219Inventory Costs in the EOQ Situation 220

Finding the EOQ 222

Sumco Pump Company Example 222

Purchase Cost of Inventory Items 223

Sensitivity Analysis with the EOQ Model 224

Reorder Point: Determining When to Order 225

CONTENTS

6.6 EOQ Without the Instantaneous ReceiptAssumption 226

Annual Carrying Cost for Production RunModel 227

Annual Setup Cost or Annual Ordering Cost 228

Determining the Optimal Production Quantity 228

Brown Manufacturing Example 228

6.7 Quantity Discount Models 230

Brass Department Store Example 232

6.8 Use of Safety Stock 233

6.9 Single-Period Inventory Models 240

Marginal Analysis with Discrete Distributions 241

Cafe du Donut Example 242

Marginal Analysis with the NormalDistribution 242

Newspaper Example 243

ABC Analysis 245

Dependent Demand: The Case for MaterialRequirements Planning 246

Material Structure Tree 246

Gross and Net Material Requirements Plan 247

Two or More End Products 249

6.12 Just-in-Time Inventory Control 250

6.13 Enterprise Resource Planning 252

Summary 252 Glossary 252 Key Equations 253Solved Problems 254 Self-Test 257 DiscussionQuestions and Problems -258 Case Study:Martin-Pullin Bicycle Corporation 265Bibliography 266

6.10

6.11

7.8 Sensitivity Analysis 296

High Note Sound Company 298

Changes in the Objective Function Coefficient 298

QM for Windows and Changes in ObjectiveFunction Coefficients 299

Excel Solver and Changes in Objective FunctionCoefficients 300

Changes in the Technological Coefficients 300

Changes in the Resources or Right-Hand-SideValues 302

QM for Windows and Changes in Right-Hand-Side Values 303

Excel Solver and Changes in Right-Hand-SideValues 305

Summary 305 Glossary 305 SolvedProblems 306 Self-Test 311 DiscussionQuestions and Problems 312 Case Study:Mexicana Wire Works 320 Bibliography 322

Appendix 7.1 Excel QM 322

CHAPTERS Linear Programming Applications 3278.1 Introduction 328

8.2 Marketing Applications 328

Media Selection 328

Marketing Research 329

8.3 Manufacturing Applications 332

Production Mix 332

Production Scheduling 333

Appendix 6.1

CHAPTER 7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

Inventory Control with QMfor Windows 266

Linear Programming Models: Graphicaland Computer Methods 269

Introduction 270

Requirements of a Linear ProgrammingPrnhlem ?7fliiuuieiii z./u

Formulating LP Problems 271

Flair Furniture Company 272Graphical Solution to an LP Problem 273

Graphical Representation of Constraints 273

Isoprofit Line Solution Method 277Corner Point Solution Method 280

Slack and Surplus 282

Solving Flair Furniture's LP Problem UsingQMFor Windows and Excel 283Using QM for Windows 283

Using Excel's Solver Command to Solve1 P Prr»hlpmc 784Lr rlOUlCIlla 1̂O4

Solving Minimization Problems 290

Holiday Meal Turkey Ranch 290

Four Special Cases in LP 294

No Feasible Solution 294

Unboundedness 295

Redundancy 295

Alternate Optimal Solutions 296

8.4

8.5

8.6

8.7

CHAPTER 9

9.1

9.2

9.3

9.4

Employee Scheduling Applications 337

Labor Planning 337

Financial Applications 339

Portfolio Selection 339

Truck Loading Problem 342

Ingredient Blending Applications 344

Diet Problems 344

Ingredient Mix and Blending Problems 345

Transportation Applications 347

Shipping Problem 347Summary 350 Self-Test 350 Problems 351Case Study: Chase Manhattan Bank 359Bibliography 359

Transportation and AssignmentModels 361

Introduction 362

The Transportation Problem 362

Linear Program for the TransportationExample 362

A General LP Model for TransportationProblems 363

The Assignment Problem 364

Linear Program for Assignment Example 365

The Transshipment Problem 366

Linear Program for Transshipment Example 367

10 CONTENTS

9.5 The Transportation Algorithm 368Developing an Initial Solution: Northwest

Corner Rule 370

Stepping-Stone Method: Finding a Least-CostSolution 372

9.6 Special Situations with the TransportationAlgorithm 378Unbalanced Transportation Problems 378

Degeneracy in Transportation Problems 379

More Than One Optimal Solution 382

Maximization Transportation Problems 382

Unacceptable or Prohibited Routes 382

Other Transportation Methods 382

9.7 Facility Location Analysis 383

Locating a New Factory for Hardgrave MachineCompany 383

9.8 The Assignment Algorithm 385

The Hungarian Method (Flood's Technique) 386

Making the Final Assignment 389

9.9 Special Situations with the AssignmentAlgorithm 391

Unbalanced Assignment Problems 391

Maximization Assignment Problems 391

Summary 393 Glossary 393 SolvedProblems 394 Self-Test 400 DiscussionQuestions and Problems 401 Case Study:Andrew-Carter, Inc. 411 Case Study: OldOregon Wood Store 412 Bibliography 413

Appendix 9.1 Using QM for Windows 413

CHAPTER 10 Integer Programming, Goal Programming,and Nonlinear Programming 415


10.2 Integer Programming 416

Harrison Electric Company Example of IntegerProgramming 416

Using Software to Solve the Harrison IntegerProgramming Problem 418

Mixed-Integer Programming ProblemExample 420

10.3 Modeling with 0-1 (Binary) Variables 422

Capital Budgeting Example 422

Limiting the Number of Alternatives Selected 424

Dependent Selections 424

Fixed-Charge Problem Example 424

Financial Investment Example 425

10.4 Goal Programming 426

Example of Goal Programming: Harrison ElectricCompany Revisited 428

Extension to Equally Important Multiple Goals 429

Ranking Goals with Priority Levels 429

Goal Programming with Weighted Goals 430

10.5 Nonlinear Programming 431

Nonlinear Objective Function and LinearConstraints 432

Both Nonlinear Objective Function andNonlinear Constraints 433

11.1

11.2

11.3

11.4

12.1

12.2

12.3

12.4

12.5

Appendix 12.1

Linear Objective Function with NonlinearConstraints 434

Summary 435 Glossary 435Solved Problems 436 Self-Test 439 DiscussionQuestions and Problems 439 Case Study:Schank Marketing Research 445 Case Study:Oakton River Bridge 445 Bibliography 446

Network Models 449Introduction 450

Minimal-Spanning Tree Problem 450

Maximal-Flow Problem 453

Maximal-Flow Technique 453

Linear Program for Maximal Flow 458

Shortest-Route Problem 459

Shortest-Route Technique 459

Linear Program for Shortest-Route Problem 461

Summary 464 Glossary 464Solved Problems 465 Self-Test 467Discussion Questions and Problems 468Case Study: Binder's Beverage 475 Case Study:Southwestern University Traffic Problems 476Bibliography 477

Project Management 479

Introduction 480

PERT/CPM 480

General Foundry Example of PERT/CPM 481

Drawing the PERT/CPM Network 482

Activity Times 483

How to Find the Critical Path 484

Probability of Project Completion 489

What PERT Was Able to Provide 491

Using Excel QM for the General FoundryExample 491

Sensitivity Analysis and Project Management 491

PERT/Cost 493

Planning and Scheduling Project Costs:Budgeting Process 493

Monitoring and Controlling Project Costs 497

Project Crashing 499

General Foundary Example 500

Project Crashing with Linear Programming 500

Other Topics in Project Management 504

Subprojects 504

Milestones 504

Resource Leveling 504

Software 504

Summary 504 Glossary 505Key Equations 505 Solved Problems 506Self-Test 507 Discussion Questions andProblems 508 Case Study: Project Management:Cost, Quality and Time Trade-Off in a ThaiConstruction Company 514 Case Study: FamilyPlanning Research Center of Nigeria 515Bibliography 516

Project Management with QMfor Windows 517

CONTENTS 11

CHAPTER 13 Waiting Lines and Queuing TheoryModels 519


13.2 Waiting Line Costs 520

Three Rivers Shipping Company Example 521

13.3 Characteristics of a Queuing System 521

Arrival Characteristics 521

Waiting Line Characteristics 522

Service Facility Characteristics 523

Identifying Models Using Kendall Notation 523

13.4 Single-Channel Queuing Model with PoissonArrivals and Exponential Service Times(M/M/l) 526

Assumptions of the Model 526

Queuing Equations 526

Arnold's Muffler Shop Case 527

Enhancing the Queuing Environment 531

13.5 Multichannel Queuing Model with PoissonArrivals and Exponential Service Times(M/M/m) 531

Equations for the Multichannel QueuingModel 532

Arnold's Muffler Shop Revisited 532

13.6 Constant Service Time Model (M/D/l) 534

Equations for the Constant Service TimeModel 535

Garcia-Golding Recycling, Inc. 535

13.7 Finite Population Model (M/M/l with FiniteSource) 536

Equations for the Finite Population Model 537

Department of Commerce Example 537

13.8 Some General Operating CharacteristicRelationships 539

13.9 More Complex Queuing Models andthe Use of Simulation 539

Summary 540 Glossary 540 Key Equations541 Solved Problems 542 Self-Test 544Discussion Questions and Problems 545 CaseStudy: New England Foundry 550 Case Study:Winter Park Hotel 551 Bibliography 552

Appendix 13.1

CHAPTER 1 414.1

14.2

14.3

14.4

14.5

Using QMfor Windows 552

Simulation Modeling 553Introduction 554

Advantages and Disadvantagesof Simulation 555

Monte Carlo Simulation 556

Harry's Auto Tire Example 556

Using QM for Windows for Simulation 561

Simulation with Excel Spreadsheets 561

Simulation and Inventory Analysis 565Simkin's Hardware Store 565

Analyzing Simkin's Inventory Costs 568

Simulation of a Queuing Problem 570

Port of New Orleans 570

Using Excel to Simulate the Port of New OrleansQueuing Problem 571

14.6 Simulation Model for a MaintenancePolicy 573

Three Hills Power Company 573

Cost Analysis of the Simulation 577

14.7 Other Simulation Issues 577

Two Other Types of Simulation Models 577

Verification and Validation 579

Role of Computers in Simulation 580

Summary 580 Glossary 580Solved Problems 581 Self-Test 584Discussion Questions and Problems 585Case Study: Alabama Airlines 590 Case Study:Statewide Development Corporation 591Bibliography 592

B Markov Analysis 59315.1 Introduction 594

15.2 States and State Probabilities 594

The Vector of State Probabilities for ThreeGrocery Stores Example 595

15.3 Matrix of Transition Probabilities 596

Transition Probabilities for the Three GroceryStores 597

15.4 Predicting Future Market Shares 597

15.5 Markov Analysis of Machine Operations 598

15.6 Equilibrium Conditions 599

15.7 Absorbing States and the FundamentalMatrix: Accounts Receivable Application 602

Summary 606 Glossary 607 Key Equations607 Solved Problems 607 Self-Test 611 'Discussion Questions and Problems 611Case Study: Rentall Trucks 615 Bibliography 617

Appendix 15.1Appendix 15.2

CHAPTER 1 616.116.216.3

16.4

16.5

Appendix 16.1

Markov Analysis with QMfor Windows 6\Markov Analysis With Excel 619

Statistical Quality Control 621Introduction 622Defining Quality and TQM 622Statiscal Process Control 623Variability in the Process 623

Control Charts for Variables 625

The Central Limit Theorem 625

Setting x-Chart Limits 626

Setting Range Chart Limits 629

Control Charts for Attributes 630p-Charts 630

c-Charts 633

Summary 634 Glossary 634 Key Equations634 Solved Problems 635 Self-Test 636Discussion Questions and Problems 637Bibliography 639

Using QMfor Windows for SPC 639

12 CONTENTS

APPENDICES 641APPENDIX A Areas Under the Standard

Normal Curve 642

APPENDIX B Binomial Probabilities 644

APPENDIX C Values of e~A for use in the PoissonDistribution 649

APPENDIX D ^Distribution Values 650

APPENDIX E Using POM-QM for Windows 652

APPENDIX f Using Excel QM and Excel Add-Ins 655

APPENDIX G Solutions to Selected Problems 656

APPENDIX H Solutions to Self-Tests 659

INDEX 661

ONLINE MODULES

MODULE 1 Analytic Hierarchy Process Ml-1

Ml.l Introduction Ml-2

Ml.2 Multifactor Evaluation Process Ml-2

Ml.3 Analytic Hierarchy Process Ml-4

Judy Grim's Computer Decision Ml-4

Using Pairwise Comparisons Ml-5

Evaluations for Hardware Ml-7

Determining the Consistency Ratio Ml-7

Evaluations for the Other Factors Ml-9

Determining Factor Weights Ml-10

Overall Ranking Ml-10

Using the Computer to Solve Analytic HierarchyProcess Problems M1 -10

Ml.4 Comparison of Multif actor Evaluation andAnalytic Hierarchy Processes Ml -11

Summary Ml-12 Glossary Ml-12 KeyEquations Ml-12 Solved Problems Ml-12 Self-Test Ml-14 Discussion Questions and ProblemsMl-14 Bibliography Ml-16

Appendix Ml. 1 Using Excel for the Analytic Hierarchy ProcessMl-16

MODULE 2 Dynamic Programming M2-1M2.1 Introduction M2-2

M2.2 Shortest-Route Problem Solved using DynamicProgramming M2-2

M2.3 Dynamic Programming Terminology M2-6

M2.4 Dynamic Programming Notation M2-8

M2.5 Knapsack Problem M2-9

Types of Knapsack Problems M2-9

Roller's Air Transport ServiceProblem M2-9

Summary M2-16 Glossary M2-16 KeyEquations M2-16 Solved Problems M2-17Self-Test M2-19 Discussion Questionsand Problems M2-20 Case Study: UnitedTrucking M2-22 Internet Case Study M2-22Bibliography M2-23

MODULE 3 Decision Theory and the NormalDistribution M3-1

M3.1 Introduction M3-2

M3.2 Break-Even Analysis and the NormalDistribution M3-2

Barclay Brothers Company's New ProductDecision M3-2

Probability Distribution of Demand M3-3

Using Expected Monetary Value to Make aDecision M3-5

M3.3 Expected Value of Perfect Information and theNormal Distribution M3-6

~ Opportunity Loss Function M3-6

Expected Opportunity Loss M3-6

Summary M3-8 Glossary M3-8Key Equations M3-8 Solved ProblemsM3-9 Self-Test M3-10 DiscussionQuestions and Problems M3-10Bibliography M3-12

Appendix M3.1 Derivation of the Break-EvenPoint M3-12

Appendix M3.2 Unit Normal Loss Integral M3-13

MODULI 4 Game Theory M4-1 ,


M4.2 Language of Games M4-2

M4.3 The Minimax Criterion M4-3

M4.4 Pure Strategy Games M4-4

M4.5 Mixed Strategy Games M4-5

M4.6 Dominance M4-7

Summary M4-7 Glossary M4-8Solved Problems M4-8 Self-Test M4-10Discussion Questions and Problems M4-10Bibliography M4-12

Appendix M4.1

MODULE 5

M5.1

M5.2

M5.3

M5.4

Game Theorywith QM for Windows M4-12

Mathematical Tools: Determinantsand Matrices M5-1

Introduction M5-2

Matrices and MatrixOperations M5-2

Matrix Addition and Subtraction M5-2

Matrix Multiplication M5-3

Matrix Notation for Systemsof Equations M5-6

Matrix Transpose M5-6

Determinants, Cofactors,andAdjoints M5-7Determinants M5-7

Matrix of Cofactors and Adjoint M5-9

Finding the Inverse of a Matrix M5-10

Summary M5-12 Glossary M5-12Key Equations M5-12 Self-Test M5-13Discussion Questions and Problems M5-13Bibliography M5-14

AppendixM5.1 Using Excel for Matrix Calculations M5-15

MODULE 6 Calculus-Based Optimization M6-1M6.1 Introduction M6-2

M6.2 Slope of a Straight Line M6-2

M6.3 Slope of a Nonlinear Function M6-3

M6.4 Some Common Derivatives M6-5

Second Derivatives M6-6

M6.5 Maximum and Minimum M6-6

M6.6 Applications M6-8

Economic Order Quantity M6-8

Total Revenue M6-9

Summary M6-10 Glossary M6-10 KeyEquations M6-10 Solved Problem M6-11Self-Test M6-11 Discussion Questions andProblems M6-12 Bibliography M6-12

MODULE 7 Linear Programming: The SimplexMethod M7-1 .


M7.2 How to Set Up the Initial SimplexSolution M7-2

Converting the Constraints to Equations M7-3

Finding an Initial Solution Algebraically M7-3

The First Simplex Tableau M7-4

M7.3 Simplex Solution Procedures M7-8

M7.4 The Second Simplex Tableau M7-9

Interpreting the Second Tableau M7-12

M7.5 Developing the Third Tableau M7-13

M7.6 Review of Procedures for Solving LPMaximization Problems M7-16

M7.7 Surplus and Artificial Variables M7-16

Surplus Variables M7-17

Artificial Variables M7-17

Surplus and Artificial Variables in the ObjectiveFunction M7-18

/CONTENTS 13

M7.8 Solving Minimization Problems M7-18

The Muddy River Chemical CompanyExample M7-18

Graphical Analysis M7-19

Converting the Constraints and ObjectiveFunction M7-20

Rules of the Simplex Method for MinimizationProblems M7-21

First Simplex Tableau for the Muddy RiverChemical Corporation Problem M7-21

Developing a Second Tableau M7-23

Developing a Third Tableau M7-24

Fourth Tableau for the Muddy River ChemicalCorporation Problem M7-26

M7.9 Review of Procedures for Solving LPMinimization Problems M7-27

M7.10 Special Cases M7-28

Infeasibility M7-28

Unbounded Solutions M7-28

Degeneracy M7-29

More Than One Optimal Solution M7-30

M7.11 Sensitivity Analysis with the SimplexTableau M7-30

High Note Sound Company Revisited M7-30

Changes in the Objective FunctionCoefficients M7-31

Changes in Resources or RHS Values M7-33

M7.12 The Dual M7-35

Dual Formulation Procedures M7-37

Solving the Dual of the High Note SoundCompany Problem M7-37

M7.13 Karmarkar's Algorithm M7-39

Summary M7-39 Glossary M7-39 KeyEquation M7-40 Solved Problems M7-40Self-Test M7-42 Discussion Questions andProblems M7-45 Bibliography M7-54

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