Optimization Using Linear Programming

This book is designed for engineers, mathematicians, computer scientists, financial analysts, and anyone interested in using numerical linear algebra, matrix theory, and game theory to solve applied problems efficiently. It emphasizes solving linear programming problems with software like MS-Excel, Mathematica, MATLAB, WinQSB, and LINDO, while providing the necessary definitions and theorems for mastering theoretical aspects. The journey begins with basics of linear algebra using MS-Excel, followed by an introduction to linear programming problems and the graphical method. It then delves into the simplex method, duality, and sensitivity analysis. The course covers transportation, transshipment, assignment problems, and concludes with game theory. Each chapter builds on the previous one, ensuring a comprehensive understanding of the topics. Understanding these concepts is crucial for solving complex applied problems. This book transitions readers from basic to advanced techniques in numerical linear algebra and linear programming, combining theoretical knowledge with practical applications. It is an essential resource for mastering these topics and maximizing efficiency in problem-solving.