Linear Programming and Simplex Method

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Submitted By devharajan
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Pages 8
LINEAR PROGRAMING AND SIMPLEX
METHOD
Devharajan Rangarajan

Department of Electronic Engineering
National University of Ireland, Maynooth

devharajan.rangarajan.2016@mumail.ie
Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization.
This paper focuses on one such optimization technique known as
Linear programming and one of its method known as Simplex method in detail with examples.

cTx = c1x1 + · · · + cnxn

The subject of linear programming can be defined quite concisely. It is concerned with the problem of maximizing or minimizing a linear function whose variables are required to satisfy a system of linear constraints, a constraint being a linear equation or inequality. The subject might more appropriately be called linear optimization. Problems of this sort come up in a natural and quite elementary way in many contexts but especially in problems of economic planning.

(or Ax ≤ b)

I. INTRODUCTION

Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labour, and then determining the "best" production levels for maximal profits under those conditions.
In "real life", linear programming is part of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources. These "real life" systems can have dozens or hundreds of variables, or more. In algebra, though, you'll only work with the simple (and graphable) two-variable linear…...

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