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Topics in Linear Programming and Games Theory
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Book ID : NBC507
ISBN No. : 81-7211-226-2
Book Name : Topics in Linear Programming and Games Theory
Author/s name/s : Bandopadhyaya Lakshmisree
Publisher Name : Northern Book Centre
Publishing Year : 2016
Book Price (Printed) : INR 300   
Book Price (Our Price) : INR 270   
Book Size : 25 × 19 cm.
Book Page : xviii + 334
Book Weight : 500 gm


   Post Review
Book Summary
  • This book gives methodical and step-by-step explanation of the Simplex Method which is missing in most of the available books.
  • The book goes on as a teacher explaining and simplifying the topics to a student.
  • All the university question paper problems with 74 examples and 81 exercises illustrate the methodology.
  • Problems solved by Graphical Method are explained with neat and accurate graphs.
  • Twenty-One Theorems with proofs and corollaries will facilitate logical understanding of the subject.
  • Detailed explanations are given to make the reader confident about the subject.
Book Content

Preface

Introduction

SECTION 1 – Preliminaries

1. Linear Programming Problems

  • Introduction

  • Mathematical formulation of Practical Linear Programming Problems (LPP)

  • Standardisation of LPP by Introducing Slack and Surplus Variables

  • Graphical Method of Solving a Linear Programming Problem (LPP

  • Examples 1.1 to 1.7

  • Nature of Solutions of LPP

  • Exercises (1 –15)

  • Preliminaries

  • Vector Space

  • Row Space and Column Space

  • Rank of a Matrix

  • Row Rank of a Matrix

  • Column Rank of a Matrix

  • Linear Independence

  • Linear Dependence

  • Useful Results of Linear Algebra

  • Results I to III

  • Basis

  • Properties

  • Basic Solution

  • Examples 1.8 to 1.9

  • Important Definitions

  • Hyperplane

  • Hypersphere

  • e-neighbourhood

  • Interior Point

  • Boundary Point8

  • Open Set

  • Closed Set

  • Bounded Set

  • Convex Set

  • Convex Combination of Finite Number of Points

  • Convex Polyhedron

  • Simplex

  • Convex Hull of a Set A

  • Theorems on Covex Set, Feasible Region, Basic Feasible Solution and Convex Hull

  • Theorems 1.1 to 1.2

  • Lemmas I and II

  • Theorem 1.3

  • Examples 1.10 to 1.12

  • Convex Hull of Finite Set

  • Theorem 1.4

  • Examples 1.13 to 1.16 (Convex and Non-convex Sets)

  • Euclidean Plane and Feasible Region of lpp

  • Extreme Point

  • Theorem 1.5

  • Half Spaces4

  • Supporting hyperplane

  • Optimal hyperplane

  • Theorem 1.6

  • Analytical Results

  • Results I to IV

  • Optimal Solution and Extreme Points

  • Theorem 1.7

  • Optimality Criterion

  • Some Notations

  • Theorem 1.8

  • Corollary  

  • Unbounded Solution

  • Theorem 1.9

  • Corollary

  • Improving a Basic Feasible Solution (BFS)

  • Theorem 1.10

  • Corollary

  • Alternate Optima

  • Theorem 1.11

  • Non-basic Alternate Optimal Solution

  • Examples 1.17 to 1.18

  • Miscellaneous Exercises (1-10)

 

SECTION 2 – Solution Techniques

2. Simplex Algorithm

  • Pre-requisites

  • Formation of a New Table by Changing the Basis

  • Simplex Algorithm

  • Application to Problems with Slack Variables Only

  • Example 2.1

  • Charnes’ M-Technique for Problems with Surplus and Artificial Variables

  • Application of Simplex Method to Problems with Surplus and

  •   Artificial Variables

  • Examples 2.2 to 2.10

  • Two-Phase method
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