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Linear Programming

Linear Programming, also known as linear optimization, is a method that utilizes mathematical models to achieve the best possible outcomes or results. These models are based on linear relationships.

The concept behind linear programming is that if a system can be represented by a mathematical model and its objective can be quantified, a computational method can be devised to determine the optimal course of action among available alternatives. This application of mathematical models is referred to as linear programming.

Linear programming finds applications in diverse fields such as the military, economics, and industry. By using linear inequalities and equations, solutions are developed through linear programming methods.

The topics covered under Linear Programming include:

1. Definition of Linear Programming
2. Classification of Programming Problems
3. Mathematical Programming and Automation
4. Origins of Linear Programming
5. Economic Models and Linear Programming
6. Industrial Applications of Linear Programming
7. Formulating Linear Programming Model
8. Linear Equation and Inequality Systems
9. Simplex Method
10. Proof Of Simplex Algorithm and Duality Theorem
11. Simplex Method Using Multipliers
12. Finiteness Of Simplex Method Under Perturbation
13. Variants Of Simplex Algorithm
14. Geometry Of Linear Programs
15. Pivoting, Vector Spaces, Matrices, and Inverses
16. Price Concept in Linear Programming
17. Games And Linear Programs
18. Classical Transportation Problem
19. Optimal Measurement and Other Distribution Problems
20. Transshipment Problem
21. Variables With Upper Bounds
22. Maximal Flows in Networks
23. Convex Programming
24. Decomposition Principle of Linear Programs
25. Uncertainty

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