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Linear Programming has progressed a great deal during last two decades. It is becoming increasingly sophisticated with the availability of Computer facilities and infusion of new concepts. The text of this book has been presented in easy and simple language. Throughout the text, the two streams theory and technique run side by side. Each technique is preceded by the relevant theory followed by suitable examples. A large number of important problems mostly drawn from University examination papers has been included. Contents, 1. VECTORS AN Context (SIMPLEX METHOD) : Origin and Development, Requirements of Linear Programming, Scope of Linear Programming, Some Basic Concept an Matrical and Linear Algebra, Matrix, Special Types of Matrices, Submatrices of a Matrix, Equality of Two Matrices, Addition of Matrices, Properties of Matrix Addition, Multiplication of a Matrix by a Scalar, Multiplication of Two Matrices, Properties of Matrix Multiplication, Determinant of a Square Matrix, Non-Singular and Singular Matrices, Transpose of a Matrix, Adjoint or Adjugate of a Square Matrix, Invertible Matrices : Inverse or Reciprocal of a Matrix, Vectors, Linear Dependence and Linear Independence of Vectors, A Vector as a Linear Combination of Vectors, Systems of Linear Non-Homogeneous Equations, Condition For a System of n Equations in n Unknowns to Have a Unique Solution, Working Rule For Finding the Solution of the Equation AX = B, Some Useful Results of Linear Algebra, Linear Programming an Linear Programming Problem, Basic Requirements of a Linear Programming Problem (L.P.P.), Mathematical Description of a General Linear Programming Problem, Mathematical Formulation of a Linear Programming Problem, Slack and Surplus Variables, Formulation as a Linear Programming Problems, Some Important Definitions and Results, Solution of Simultaneous Linear Inequations, Graphical Method to Solve a Linear Programming Problem, Limitations of the Graphical Method, Applications of Linear Programming Technique, Limitations of Linear Programming, Advantages of Linear Programming, Basic Solution (B.S.). 2. VECTORS AND CONVEX SETS : Vectors, Linear Combination of Vectors, Definitions, Convex Sets and Their Properties, Convex Combination, Convex Set, Extreme Point of a Convex Set, Convex Hull, Convex Function, Convex Polyhedron, Some Important Theorems, Analytical Method. 3. SIMPLEX METHOD (THEORY AND APPLICATION) : Introduction, Some Definitions and Notations, Fundamental Theorem of Linear Programming, Reduction of Feasible Solution to Basic Feasible Solution, To Determine Improved B.F.S. from a Given B.F.S., Conditions for the Existence of Unbounded Solution, Condition for Improved Basic Feasible Solution to Become Optimal, Alternative Optimal Solutions, Inconsistency and Redundancy in Constraint Equations, To Determine Starting B.F.S., Computational Procedure Simplex Method, Artificial Variables Technique, Computational Procedure of Two Phase Method, L.P.P. Having Unbounded Solution, Solution of Simultaneous Linear Equations by Simplex Method, Inverse of a Matrix by Simplex Method, To Compute the Inverse of a Matrix Whose one Column is Different from that of a Matrix Whose Inverse is Known. Printed Pages: 224. Buchnummer des Verkäufers 59097
Titel: Text Book of Linear Programming-II
Verlag: Discovery Publishing House Pvt. Ltd.