Precize Linear Programming

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The present book is meant for the students who opt the paper of Linear Programming. It is also meant for those who are appearing in various competitive examinations.

The entire subject matter has been arranged in a simple, systematic, graded, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Exercises have been given in each chapter to provide the students with an opportunity of practice.


CONTENTS : Linear Programming and examples, Convex Sets, Hyperplanes, Open and Closed half-spaces, Feasible, Basic Feasible and Optimal Solutions, Extreme Points & graphical methods. Simplex method, Charnes-M method, Two phase method, Determination of Optimal solutions, unrestricted variables, Duality theory, Dual linear Programming Problems, fundamental properties of dual Problems, Complementary slackness, Unbounded solution in Primal. Dual Simplex Algorithm, Sensitivity analysis.

Parametric Programming, Revised Simplex method, Transportation Problems, Balanced and unbalanced Transportation problems, U-V method, Paradox in Transportation problem, Assignment problems, Integer Programming problems: Pure and Mixed Integer Programming problems, 0-1 programming problem, Gomary’s Algorithm, Branch & Bound Technique, Travelling salesman Problem.

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