Lecture 3

# Lecture 3 - The Simplex Method Solving the Canonical LP...

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The Simplex Method Solving the Canonical LP models HW1 on Blackboard

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Setting a LP model for the Simplex Let’s reconsider an earlier model: Max Z = 3 x 1 + 5 x 2 st: x 1 4 2 x 2 12 3 x 1 + 2 x 2 18 x 1 0 x 2 0 Now, add a set of “slack” variables to the LHSs: Max Z = 3 x 1 + 5 x 2 st: x 1 +x 3 = 4 2 x 2 +x 4 = 12 3 x 1 + 2 x 2 +x 5 = 18 x 1 0, x 2 0, x 3 0, x 4 0, x 5 0 These models are equivalent!
Move the RHS of the objective function to the left: Max Z Z -3 x 1 - 5 x 2 = 0 x 1 + x 3 = 4 2 x 2 +x 4 = 12 3 x 1 + 2 x 2 +x 5 = 18 x 1 0, x 2 0, x 3 0, x 4 0, x 5 0 This set of equations is equivalent to the original LP model!

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Note the following observations: 1. We expanded the dimensions of the problem from 2 to 5. Now, the constraints are all equations instead of inequalities and therefore, it is easier to obtain a feasible solution by solving the equations simultaneously. 2.
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## This document was uploaded on 11/04/2011 for the course MME 414 at Miami University.

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Lecture 3 - The Simplex Method Solving the Canonical LP...

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