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DUALITY THEORY IN LINEAR PROGRAMMING AND APPLICATION

CHAPTER ONE

GENERAL INTRODUCTION

Many people rank the development of linear programming among the most important scientific advances of the mid-twentieth century, and we must agree with this assessment. It’s impact since 1950 till date have been extra-ordinary.Today, it is a standard tool that has saved thousands and millions of naira for companies or even moderate size in industrialized countries of the World and other uses of it is widely spreading to other sectors. Duality theory seeks to find a related solution to a primal problem in linear programming. There one can afford to define duality as “as associated linear program of a linear programming problems such that a solution to the primal linear program also gives a solution to it’s dual”.

Linear programming deals with the problem of allocating limited resources among competing activities in the best possible way. This problem of allocation can arise whenever one must select a level of certain activities that can compete for scarce resources necessarily to perform those activities. The variety of the situations to which this description applies is diverse ranging from the allocation of product facilities to product and allocation of national resources to domestic needs; from portfolio selection to the shipping patterns selection, agricultural planning to the design of radiation therapy, and so on. However, the one common ingredient in each of these situations is the necessity for allocating resources to activities.

Linear programming uses mathematical models to describe the problem concerned. The adjective “linear” means that all the mathematical function in this model are required to be linear functions, the word “programming” does not refer here to computer programming rather it is essentially a synonym for planning.

Thus, linear programming involves the planning of activities to obtain optimal results that reach specified goal best (according to the mathematical model) among all feasible alternatives.

Owing to the importance of linear programming, this project work is devoted to it and the focus is on the “DUALITY THEORY IN LINEAR PROGRAMMING AND APPLICATION USING JONACON INVESTMENT AS A CASE OF STUDY.

AIMS AND OBJECTIVE OF STUDY

  1. The major aims and objectives of this work is the formulation of duality problems of JONACON INVESTMENT, a concrete industry located at kwata junction along Enugu-Onitsha expressway in Anambra State which produces electric poles of big and medium sizes and culvert rings of medium, small and big sizes uses for construction of culvert and bridges.
  2. We shall observe that “duality” sometimes shortens problem solving time and gives a clue to the potentials for increased revenue returns.

SCOPE OF STUDY

As the topic of this project work suggests; “The duality theory and it is application in linear programming”. We will be studying in details.

  1. The meaning of linear programming and its theorems.
  2. Formulation of linear programming using Duality.

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Topic: DUALITY THEORY IN LINEAR PROGRAMMING AND APPLICATION –A CASE OF JONACON INVESTMENT, AWKA

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