Transcription of Math 407 — Linear Optimization 1 Introduction
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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.
In modeling this example, we will review the four basic steps in the development of an LP model: 1. Identify and label the decision variables. ... geometric structure more fully as the course evolves. For the moment, note that the solution to the Plastic Cup Factory problem lies at a corner point of the feasible region. Indeed, it is
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