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OutlineMaximization Case
Simplex Method in Maximization Case
Esra Nur Sahin & Semih Gumusbas
Marmara University
October 19, 2015
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
1 Maximization CaseExampleConverting The Constraints To EquationsSimplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Example
Example:
Use the simplex method to find the maximum value of
zmax = 60x1 + 43x2
subject to the constraints;
3x1 + x2 ≥ 93x1 + 2x2 = 12x1 + 2x2 ≤ 10
where x1, x2 ≥ 0.
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2 +A2 = 12
x1 + 2x2 +S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2
+A2 = 12
x1 + 2x2 +S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2 +A2 = 12
x1 + 2x2 +S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2 +A2 = 12
x1 + 2x2
+S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2 +A2 = 12
x1 + 2x2 +S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Constructing Equations:
3x1 + x2 −S1 + A1 = 9
3x1 + 2x2 +A2 = 12
x1 + 2x2 +S3 = 10
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1
− M.A1 − M.A2 + 0.S3
where
x1, x2,S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1 − M.A1
− M.A2 + 0.S3
where
x1, x2,S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2
+ 0.S3
where
x1, x2,S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2 + 0.S3
where
x1, x2,S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2 + 0.S3
where
x1, x2, S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Converting The Constraints To Equations
Zmax :
zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2 + 0.S3
where
x1, x2, S1,A1,A2,S3 ≥ 0
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Calculating Zj :
Zj =∑
(the coefficient of basic variable) ∗ aij
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Calculating New Values:
New row value = Current row entry - ( the current value of thepivot column in its row) * (the new divided value in the pivot rowin its column)
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
OutlineMaximization Case
ExampleConverting The Constraints To EquationsSimplex Tableau
Simplex Tableau
Esra Nur Sahin & Semih Gumusbas Simplex Method in Maximization Case
