# Linear Programming Study Materials 2021 – Download E-Books PDF & Imp Questions

Download Linear Programming Study Materials 2021. In this article, we are going to provide  Study Notes for the School of Sciences. Students of B.Sc & M.Sc can download these Study Materials which will be useful for their Exam Preparation. This subject will come for Mathematical students. Our website Exams Time has come up with the best materials for the main concepts of Basic Mathematics and Optimization, Simplex Method, Games Theory, etc. Continue reading the below article to download the study books. ## Linear Programming Study Materials

 Name of the Subject Linear Programming Category School of Sciences Useful for B.Sc, M.Sc (Mathematics) Course Type Under Graduation and Post Graduation Courses Article on Linear Programming Study Materials 2021 Study Material Format PDF Download Other Study Materials Click Here

### Linear Programming Study Books

Download Unit wise PDFs of Linear Programming Study Materials :

Download Unit wise PDFs of Linear Programming Study Materials :

## Chapters & Topics

The topics that are covered in this syllabus are provided here. For further more details regarding these chapters, go through the article and refer to the books given here.

Basic Mathematics and Optimization

• Optimization in more than two Variables
• Optimization in two Variables
• Inequalities and Convex Sets
• Basic Algebra

Simplex Method and Duality

• Duality Theorems
• Primal and Dual
• The Simplex Method
• Standard Form and Solutions

Special Linear Programming Problems

• The Assignment Problem
• Computational Method for the Transportation Problem
• An Initial Basic Feasible Solution of the Transportation Problem
• The Transportation Problem

Games Theory

• Games and Linear Programming
• Graphical Method and Dominance
• Games with Mixed Strategies
• Games with Pure Strategies

## Subject in the Universities

This subject will be useful to the students who are pursuing a B.Sc, M.Sc in Mathematics. The following university students can also download Linear Programming study materials :

• IGNOU
• Uttarakhand Open University
• University of Calicut
• Pondicherry University

### Subject in the Semesters

Linear Programming subject will be studied by the students in the following semesters of their respective courses :

• B.Sc Mathematics VI Semester
• M.Sc Mathematics I Year

## Unit wise PDFs

Download Unit wise PDFs of Linear Programming Study Materials :

### Important Questions

We have mentioned some of the important topics of Linear Programming subject :

• Graphical Method
• Bounded and unbounded feasible regions
• Alternative Optimum
• Notion of Convex Sets
• Extreme Points of Convex Set
• Hyper Planes and Half Spaces
• Matrices
• Algebra of Matrices
• Determinant of a Matrix
• Adjoint-of a Matrix
• Inverse of a Matrix
• Rank of a Matrix
• Notion of a Vector
• Types of Vectors
• Algebra of Vectors
• Euclidean Spaces
• Vector Spaces
• Simplex Algorithm
• Artificial Variable Method
• Mathematical Formulation of the TP
• Algebraic Method when the gay-off is a square matrix
• Reducing the rectangular matrix game to that of a Linear Programming problem Fundamental Theorem of rectangular games
• Maximize Z = 6x, + SX2 + 3×3 + 7×4 subject to the constraints
• x1 + x2 + 3×4 ≤ 50
• 2×1 + x2 + 2×3 + x4 ≤ 150
• X1 + X2 + X3 + 4×4 ≤ 80
• X1 ,x2, X3, x4 ≥ 0
• Maximize
• z = XI subject to the constraint
• X1+x2+X3 ≤ 1
• X1,X2,X3 ≥ 0
• Solve the following linear programming problem.
• Maximize Z = x1+x2+x3 subject to the constraints
• x1 ≤ 1, x2 ≤ 1, x3 ≤ 1
• X1,X2,X3 ≥ 0

## Recommended Books for Linear Programming

The books that are recommended by toppers and subject teachers are given here. Refer all the books given here for more information.

• Linear Programming: New Frontiers in Theory and Applications (Mathematics Research Developments) by Zoltán Ádám Mann
• Linear Programming by R.K. Gupta
• Linear Programming by G Hadley
• Linear Programming by S. K. Sharma

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