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Chapter 5 Section 4

# Chapter 5 Section 4 - 5.4 Simplex method maximization with...

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5.4 Simplex method: maximization  with problem constraints of the form  The procedures for the simplex method will be  illustrated through an example. Be sure to read  the textbook to fully understand all the concepts  involved.

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Example:  We will solve the same problem that was presented earlier, but this time we will  use the simplex method. We wish to maximize the Profit function subject to the  constraints below. The method introduced here can be used to solve larger  systems that are more complicated.  5 10 8 8 160 4 12 180 0; 0 P x y x y x y x y = + + +
Introduce slack variables; rewrite  objective function First step is to rewrite the system without the inequality symbols and  introduce the slack variables,    and  1 s 2 s 1 2 1 2 8 8 160 4 12 180 5 10 0 , , , 0 x y s x y s x y P x y s s + + = + + = - - + =

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Represent linear system using matrix  The variable y was replaced the variable  1 2 1 2 1 2 8 8 1 0 0 160 4 12 0 1 0 180 5 10 0 0 1 0 x x s s P s s P - - 2 x
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