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Simplex Method 2010

# Simplex Method 2010 - SimplexMethod( XinLi,, , (

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Simplex Method (algorithm explained step by step) Xin Li, Department of Mathematics, University of Central Florida In linear programming problems, it is intuitive to see that the maximum and minimum are attained at one of the vertices of the feasible set (which is determined by linear equalities and inequalities). So, an oversimplified solution is given by just saying “evaluate the linear objective function at all the vertices (a finite set of points) and pick up the largest as the maximum value and smallest as the minimum value.” This is correct in theory but when the number of variables becomes large and when the feasible set is determined by many equalities and inequalities, it will be very time consuming to find all vertices. To give an efficient way to “go through” the vertices is the main goal of the simplex method. On average, we do not have to go through all the vertices to realize that we have reached a maximum (or minimum) point (even though in the worst case – there are explicit examples – we have to exhaust all vertices). We will go through an example step by step first and then summarize our procedure as an algorithm (that carries out the simplex method). Consider the following example. Maximize 25ݔ ൅30ݔ subject to 20ݔ ൅30ݔ ൑ 690 ൅4ݔ ൑ 120 ݔ ൒0 Step 0. Put the constraints into the 2 nd primal form by introducing the slack variables: 20ݔ ൅30ݔ ൅ݕ

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Simplex Method 2010 - SimplexMethod( XinLi,, , (

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