Math 407 — Linear Optimization 1 Introduction

Math 407 Linear Optimization1 What is Optimization ?A mathematical Optimization problem is one in which some function is either maximized orminimized relative to a given set of alternatives. The function to be minimized or maximizedis called theobjective functionand the set of alternatives is called the feasible region (orconstraint region). In this course , the feasible region is always taken to be a subset ofRn(realn-dimensional space) and the objective function is a function further restrict the class of Optimization problems that we consider to Linear program-ming problems (or LPs). An LP is an Optimization problem overRnwherein the objectivefunction is a Linear function, that is, the objective has the formc1x1+c2x2+ +cnxnfor someci2Ri=1,..,n,andthefeasibleregionist hesetofsolutionstoafinitenumberof Linear inequality and equality constraints, of the formai1xi+ai2x2+ +ainxn bii=1,..,sandai1xi+ai2x2+ +ainxn=bii=s+1.

Since it is an introductory example, the Plastic Cup Factory problem is particularly easy to model. As the course progresses you will be asked to model problems of increasing diculty and complexity. In this regard, let me emphasize again that the first step in the modeling process, identification of the decision variables, is always the most ...

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  Linear, Course, Introductory, Complexity, Optimization, An introductory, Linear optimization

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