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Topics in Linear Programming and Games Theory
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

Contents

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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