simplex-algorithm-489 - Linear programming simplex method...

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Steve Bishop 2004 1 Linear programming simplex method This presentation will help you to solve linear programming problems using the Simplex tableau
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Steve Bishop 2004 2 This is a typical linear programming problem Keep left clicking the mouse to reveal the next part Subject to 3 x + 2 y + z < 10 2 x + 5 y + 3 z <15 x , y > 0 The objective function The constraints Maximise P = 2 x + 3 y + 4 z
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Steve Bishop 2004 The first step is to rewrite objective formula so it is equal to zero We then need to rewrite P = 2 x + 3 y + 4 z as: P – 2 x – 3 y – 4 z = 0 This is called the objective equation
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Steve Bishop 2004 Adding slack variables s and t to the inequalities, we can write them as equalities : Next we need to remove the inequalities from the constraints This is done by adding slack variables 3 x + 2 y + z + s = 10 2 x + 5 y + 3 z + t = 15 These are called the constraint equations
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Steve Bishop 2004 Next, these equations are placed in a tableau P x y z s t values
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Steve Bishop 2004 First the Objective equation P – 2 x 3 y 4 z = 0 P x y z s t values 1 -2 -3 -4 0 0 0
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Steve Bishop 2004 Next, the constraint equations 3 x + 2 y + z + s = 10 2 x + 5 y + 3 z + t = 15 P x y z s t values 1 -2 -3 -4 0 0 0 0 3 2 1 1 0 10 0 2 5 3 0 1 15
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Steve Bishop 2004 P x y z values 1 -2 -3 -4 0 0 0 0 3 2 1 1 0 10 0 2 5 3 0 1 15 We now have to identify the  pivot First, we find the  pivot column The pivot column is the column with the greatest  negative value in the  objective equation  
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Steve Bishop 2004 P x y z s t values 1 -2 -3 -4 0 0 0 0 3 2 1 1 0 10 0 2 5 3 0 1 15
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simplex-algorithm-489 - Linear programming simplex method...

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