Simplex Method in Maximization Case

1. Outline Maximization Case Simplex Method in Maximization Case Esra Nur S¸ahin & Semih Gümü¸sba¸s Marmara University October 19, 2015 Esra Nur S¸ahin & Semih Gümü¸sba¸s Simplex Method in Maximization Case

2. Outline Maximization Case 1 Maximization Case Example Converting The Constraints To Equations Simplex Tableau Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

3. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Example Example: Use the simplex method to find the maximum value of zmax = 60x1 + 43x2 subject to the constraints; 3x1 + x2 ≥ 9 3x1 + 2x2 = 12 x1 + 2x2 ≤ 10 where x1, x2 ≥ 0. Esra Nur S¸ahin & Semih Gümü¸sba¸s Simplex Method in Maximization Case

4. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

5. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 3x1 + 2x2 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

6. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 3x1 + 2x2 +A2 = 12 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

7. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 3x1 + 2x2 +A2 = 12 x1 + 2x2 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

8. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 3x1 + 2x2 +A2 = 12 x1 + 2x2 +S3 = 10 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

9. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Constructing Equations: 3x1 + x2 −S1 + A1 = 9 3x1 + 2x2 +A2 = 12 x1 + 2x2 +S3 = 10 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

10. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Zmax : zmax = 60x1 + 43x2 −0.S1 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

11. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Zmax : zmax = 60x1 + 43x2 −0.S1 − M.A1 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

12. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Zmax : zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

13. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Converting The Constraints To Equations Zmax : zmax = 60x1 + 43x2 −0.S1 − M.A1 − M.A2 + 0.S3 Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

14. Outline Maximization Case Example Converting The Constraints To Equations Simplex 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 S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

15. Outline Maximization Case Example Converting The Constraints To Equations Simplex 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 S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

16. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Simplex Tableau Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

20. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Simplex Tableau Calculating Zj : Zj = (the coefficient of basic variable) ∗ aij Esra Nur S¸ahin & Semih Gümü¸sba¸s Simplex Method in Maximization Case

31. Outline Maximization Case Example Converting The Constraints To Equations Simplex Tableau Calculating New Values: New row value = Current row entry - ( the current value of the pivot column in its row) * (the new divided value in the pivot row in its column) Esra Nur S¸ahin & Semih G¨um¨u¸sba¸s Simplex Method in Maximization Case

Simplex Method in Maximization Case

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