a minimisation linear programming problem (LPP), solved using simplex method (operations research: OR)

1. Minimisation Problem
LPP

4. LPP: Simplex Method
x1 x2

5. LPP: Simplex Method
x1 x2 S1 S2

6. LPP: Simplex Method
Cb BV SV x1 x2 S1 S2

7. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2

8. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
S1
S2

9. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1
0 S2

10. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1

11. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1
Zj

12. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1
Zj 0 0 0 0 0

13. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1
Zj 0 0 0 0 0
Cj-Zj

14. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1
Zj 0 0 0 0 0
Cj-Zj 8 6 0 0

15. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 S1 60 4 2 1 0
0 S2 48 2 4 0 1
Zj 0 0 0 0 0
Cj-Zj 88 6 0 0

16. LPP: Simplex Method
Cj 88 6 0 0
Cb BV SV xx11 x2 S1 S2
0 S1 60 44 2 1 0
0 S2 48 22 4 0 1
Zj 0 00 0 0 0
Cj-Zj 88 6 0 0

17. LPP: Simplex Method
Cj 88 6 0 0
Cb BV SV xx11 x2 S1 S2
0 S1 60 44 2 1 0 15
0 S2 48 22 4 0 1 24
Zj 0 00 0 0 0
Cj-Zj 88 6 0 0

18. LPP: Simplex Method
Cj 88 6 0 0
Cb BV SV xx11 x2 S1 S2
00 SS11 6060 44 22 11 00 15
0 S2 48 22 4 0 1 24
Zj 0 00 0 0 0
Cj-Zj 88 6 0 0

19. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 15 1 ½ ¼ 0 R1=R1/4
0 S2

20. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 15 1 ½ ¼ 0 R1=R1/4
0 S2 18 0 3 -½ 1 R2=R2-2R1

21. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 15 1 ½ ¼ 0
0 S2 18 0 3 -½ 1
Zj 120 8 4 2 0

22. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 15 1 ½ ¼ 0
0 S2 18 0 3 -½ 1
Zj 120 8 4 2 0
Cj-Zj 0 2 -2 0

23. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 15 1 ½ ¼ 0
0 S2 18 0 3 -½ 1
Zj 120 8 4 2 0
Cj-Zj 0 22 -2 0

24. LPP: Simplex Method
Cj 8 66 0 0
Cb BV SV x1 xx22 S1 S2
0 x1 15 1 ½½ ¼ 0
0 S2 18 0 33 -½ 1
Zj 120 8 44 2 0
Cj-Zj 0 22 -2 0

25. LPP: Simplex Method
Cj 8 66 0 0
Cb BV SV x1 xx22 S1 S2
0 x1 15 1 ½½ ¼ 0 30
00 SS22 1818 00 33 -½-½ 11 6
Zj 120 8 44 2 0
Cj-Zj 0 22 -2 0

26. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1
0 x2 6 0 1 -1/6 1/3 R2=R2/3
Zj
Cj-Zj

27. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 12 1 0 1/3 -1/6 R1=R1-½R2
0 x2 6 0 1 -1/6 1/3 R2=R2/3
Zj
Cj-Zj

28. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 12 1 0 1/3 -1/6
0 x2 6 0 1 -1/6 1/3
Zj 132 8 6 5/3 2/3
Cj-Zj

29. LPP: Simplex Method
Cj 8 6 0 0
Cb BV SV x1 x2 S1 S2
0 x1 12 1 0 1/3 -1/6
0 x2 6 0 1 -1/6 1/3
Zj 132 8 6 5/3 2/3
Cj-Zj 0 0 -5/3 -2/3

30. LPP: Simplex Method