### Introduction to Mathematical Programming

Clicking on the Chapter or Appendix in the table of contents below will link to a brief abstract of the chapter. The abstracts of the software appendices include links to relevant sites. There are also some errata. A corrected second printing is planned.

A solutions manual for the even numbered problems is nearing completion.

Preface page vii

Chapter 1 Introduction to the Problems page 1

Section 1.1 Introduction page 1
Section 1.2 Types of problems to be considered page 3
Section 1.3 Sample problems page 6
Section 1.4 Graphical solution of linear programs page 17
Section 1.5 Summary and objectives page 25

Chapter 2 Vectors and Matrices page 27

Section 2.1 Introduction page 27
Section 2.2 Vectors page 28
Section 2.3 The span of a set of vectors page 34
Section 2.4 Matrices page 38
Section 2.5 Linear independence page 47
Section 2.6 Systems of equations page 54
Section 2.7 The inverse of a matrix page 68
Section 2.8 Summary and objectives page 76

Chapter 3 Linear Programming page 81

Section 3.1 Introduction page 81
Section 3.2 Slack variables page 83
Section 3.3 The simplex algorithm page 89
Section 3.4 Basic feasible solutions and extreme points page 101
Section 3.5 Formulation examples page 111
Section 3.6 General constraints and variables page 127
Section 3.7 The dual and minimizing problems page 140
Section 3.8 Sensitivity analysis page 159
Section 3.9 Summary and objectives page 177

Chapter 4 Network Models page 181

Section 4.1 Introduction page 181
Section 4.2 The transportation problem page 187
Section 4.3 The critical path method page 209
Section 4.4 Shortest path models page 232
Section 4.5 Minimal spanning trees page 239
Section 4.6 Summary and objectives page 254

Chapter 5 Unconstrained Extrema page 257

Section 5.1 Introduction page 257
Section 5.2 Locating extrema page 258
Section 5.3 The economic lot size model and convexity page 265
Section 5.4 Location of extrema in two variables page 277
Section 5.5 Least squares approximation page 286
Section 5.6 The n-variable case page 292
Section 5.7 Summary and objectives page 398

Chapter 6 Constrained Extrema page 301

Section 6.1 Introduction page 301
Section 6.2 Two variable problems page 308
Section 6.3 More variables; more constraints page 314
Section 6.4 Problems having inequality constraints page 324
Section 6.5 The convex programming problem page 334
Section 6.6 Linear programming revisited page 351
Section 6.7 Summary and objectives page 354

Chapter 7 Integer Programming page 357

Section 7.1 Introduction page 357
Section 7.2 The knapsack problem page 360
Section 7.3 The dual simplex algorithm page 369
Section 7.4 Adding a constraint page 378
Section 7.5 Branch and bound for integer programs: page 385
Section 7.6 Basic integer programming models page 392
Section 7.7 The traveling salesman problem page 410
Section 7.8 Summary and objectives page 421

Chapter 8 Introduction to Dynamic Programming page 425

Section 8.1 Introduction to recursion page 425
Section 8.2 The longest path page 433
Section 8.3 A fixed cost transportation problem page 436
Section 8.4 More examples page 441
Section 8.5 Summary and objectives page 448

Chapter 9 Case Studies page 451

Section 9.1 Tweaking Widget's production page 452
Section 9.2 A furniture sales opportunity page 459
Section 9.3 Building storage lockers page 460
Section 9.4 The McIntire farm page 451
Section 9.5 Cylinders for beverages page 462
Section 9.6 Books by the holidays page 464
Section 9.7 Into a blind trust page 466
Section 9.8 Max's taxes page 467
Section 9.9 A supply network page 468

Appendix A Brief Introductions to LINDO and LINGO page 471

Section A.1 LINDO page 471
Section A.2 LINGO page 476

Appendix B A Brief Introduction to Maple page 481

Section B.1 The basics page 481
Section B,2 Using packages page 486

Appendix C Introduction to Texas Instruments Calculators page 493

Section C.1 A Brief Introduction to the TI-82 page 493
Section C.2 A Brief Introduction to the TI-92 page 501

Appendix D Selected Answers and Hints page 509

References page 535

Index page 539

Supplements
Solutions to the Chapter 9 Cases
Chapter 10 Compound Interest

Section 10.1 Introduction page 1
Section 10.2 Compound interest and savings page 4
Section 10.3 Present value page 19
Section 10.4 Mortgages page 25
Section 10.5 Summary and objectives page 32
Appendix A Selected Answers page 35
Index page 37

The Chapter 10 link above will lead to an abstract and a postscript version.