Liniear Programming

In: Computers and Technology

Submitted By shwetank12
Words 10505
Pages 43
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0.1.1

Linear Programming
Objectives

By the end of this unit you will be able to: • formulate simple linear programming problems in terms of an objective function to be maximized or minimized subject to a set of constraints. • find feasible solutions for maximization and minimization linear programming problems using the graphical method of solution. • solve maximization linear programming problems using the simplex method. • construct the Dual of a linear programming problem. • solve minimization linear programming problems by maximizing their Dual.

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Introduction

One of the major applications of linear algebra involving systems of linear equations is in finding the maximum or minimum of some quantity, such as profit or cost. In mathematics the process of finding an extreme value (maximum or minimum) of a quantity (normally called a function) is known as optimization . Linear programming (LP) is a branch of Mathematics which deals with modeling a decision problem and subsequently solving it by mathematical techniques. The problem is presented in a form of a linear function which is to be optimized (i.e maximized or minimized) subject to a set of linear constraints. The function to be optimized is known as the objective function . Linear programming finds many uses in the business and industry, where a decision maker may want to utilize limited available resources in the best possible manner. The limited resources may include material, money, manpower, space and time. Linear Programming provides various methods of solving such problems. In this unit, we present the basic concepts of linear programming problems, their formulation and methods of solution.

0.1.3

Formulation of linear programming problems

Mathematically, the general linear programming problem (LPP) may be stated as: Maximize or Minimize subject to Z = c1 x1 + c2 x2 + . . . +…...

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