Introduction to Mathematical Programming. Part I

This textbook is intended for students of technical and economic universities. It is a result of my teaching of mathematical programming, optimization methods and operations research to students of Czestochowa University of Technology, including Erasmus+ Program students, for over ten years. This is the first part of a planned series (an intended series), limited to the presentation of issues related to linear programming. The second part will focus on non-linear programming problems. The textbook is divided into five main chapters. Chapter 1 is a reminder of some mathematical topics (the basics of linear algebra and systems of linear equations) that will help the readers understand the material discussed. Chapter 2 considers linear programming problems from its standard form to practical, highly common, with various examples of applications at the intersection of technology and economics. In chapter 3, the transportation problem with applications will be considered. Chapter 4 deals with a special kind of linear programing, so-called integer programming. And finally, Chapter 5 shows how the Maple package can be used to solve any linear programming problems.