Chase Manhattan Bank

EXTRA RICE

Objective Function : Minimize  Z  _=  _= 8(10.11)F + 8.08(F 1 + F 2) 2) + 7.82(10P1 + 9P2 + 8P3

+ 7P4 + 6P5 + 5P6 + 4P7 - 6Q4 - 5Q5 - 4Q6 - 3Q7 - 2Q8 - Q9) Subject to : F + P1 ≥ 14 F + P1 + P2 ≥ 25

0.5F + P1 + P2 + P3 ≥ 26 0.5F + P1 + P2 + P3 + P4 ≥ 38 F + P1 + P2 + P3 + P4 + P5 - Q4 ≥ 55 F + P1 + P2 + P3 + P4+ P5 + P6 - Q4 - Q5 ≥ 60 F + P1 + P2 + P3 + P4 + P5 + P6 + P7 - Q4 - Q5 - Q6 ≥ 51 F +P1 + P2 + P3 + P4 + P5 + P6 + P7 - Q4 - Q5 - Q6 - Q7 ≥ 29 F 1 + P1 + P2 + P3 + P4 + P5 + P6+ P7 - Q4 - Q5 - Q6 - Q7 - Q8 ≥ 14 F 2 + P1 + P2 + P3 + P4 + P5 + P6 + P7 - Q4 - Q5 - Q6 - Q7 - Q8 - Q9 ≥ 9

10P1 + 9P2 + 8P3 + 7P4 + 6P5 + 5P6 + 4P7 - 6Q4-5Q5 - 4Q6 - 3Q7 - 2Q8 - Q9 ≤ 128.4

F1 + F 2 ≤ F  Q4 ≤ P1 Q5 ≤ P1 + P2 - Q4 Q6

≤ P1

+ P2 + P3 - Q4 - Q5

Q7 ≤ P1 + P2 + P3 + P4 - Q4 - Q5 - Q6 Q8 ≤ P1 + P2 + P3 + P4 + P5 - Q4 - Q5 - Q6 - Q7  Q9 ≤ P1 + P2 + P3 + P4 + P5 + P6 - Q4 - Q5 - Q6- Q7 - Q8

Q4 + Q5 + Q6 + Q7 ≥ P1 Q4 + Q5 + Q6 + Q7 + Q8 ≥ P1 + P2 Q4 + Q5 + Q + Q7 + Q8 + Q9 ≥ P1 + P2 + P3 P1 + P2 + P3 + P4 + P5 + P6 + P7= Q4 + Q5 + Q6 + Q7 + Q8 + Q9

LINEAR PROGRAMMING RESULTS

F Q6

F1 Q7

F2 Q8

P1 Q9

P2

P3 RHS

P4 Dual

P5

P6

P7

Q4

Q5

Minimize 39.1

80.88 8.08 8.08 78.2 31.28 23.46 15.64 7.82

70.38 62.56 54.74 46.92 39.1

31.28 46.92

Constraint 1 0

1 0

0 0

0 0

1 0

0 >=

0 14

0 0

0

0

0

0

Constraint 2 0

1 0

0 0

0 0

1 0

1 >=

0 25

0 0

0

0

0

0

Constraint 3 0

.5 0

0 0

0 0

1 0

1 >=

1 26

0 0 -13.8629

0

0

0

Constraint 4 0

.5 0

0 0

0 0

1 0

1 >=

1 38

1 0 -13.8629

0

0

0

Constraint 5 0

1 0

0 0

0 0

1 0

1 >=

1 55

1 1 -13.8629

0

0

-1

Constraint 6 -1

1 0

0 0

0 0

1 0

1 >=

1 60

1 1 -74.6457

1

0

-1

Constraint 7 -1

1 -1

0 0

0 0

1 0

1 >=

1 51

1 0

1

1

1

-1

Constraint 8 -1

1 -1

0 -1

0 0

1 0

1 <=

1 29

1 1 21.4914

1

1

-1

Constraint 9 -1

0 -1

1 -1

0 -1

1 0

1 >=

1 14

1 1 -8.08

1

1

-1

Constraint 10 0 -1 -1

0 -1

1 -1

1 -1

1 >=

1 9

1 1 -8.08

1

1

-1

Constraint 11 0 -5 -4

0 -3

0 -2

10 -1

9 <=

8 7 6 128.4 6.0429

5

4

-6

Solution-> 5

28.2286 0 0

SOLUTION LIST

Variable

Status Value

F

Basic 28.2286

F1

Basic 13.2286

F2

Basic 8.2286

P1

NONBasic

0

P2

NONBasic

0

P3

Basic 11.8857

P4

Basic 12

P5

Basic 2.8857

P6

Basic 5

P7

NONBasic

0

Q4

NONBasic

0

Q5

NONBasic

0

Q6

NONBasic

0

Q7

Basic 31

Q8

NONBasic

0

Q9

NONBasic

0

13.2286 0 0

8.2286 0 31 0

0 0

11.8857 12 4915.108

2.8857

surplus 1

Basic 14.2286

surplus 2

Basic 3.2286

surplus 3

NONBasic

0

surplus 4

NONBasic

0

surplus 5

NONBasic

0

surplus 6

NONBasic

0

surplus 7

Basic 9

slack 8 NONBasic

0

surplus 9

NONBasic

0

surplus 10

NONBasic

0

slack 11

NONBasic

0

Optimal Value (Z)

4915.108

Original Problem

Minimize Q5

F Q6

F1 Q7

F2 Q8

P1 Q9

P2

P3

P4

P5

P6

P7

Q4

Constraint 1 0

1 0

0 0

0 0

1 0

0 >=

0 14

0

0

0

0

0

Constraint 2 0

1 0

0 0

0 0

1 0

1 >=

0 25

0

0

0

0

0

Constraint 3 0

0.5 0

0 0

0 0

1 0

1 >=

1 26

0

0

0

0

0

Constraint 4 0

0.5 0

0 0

0 0

1 0

1 >=

1 38

1

0

0

0

0

Constraint 5 0

1 0

0 0

0 0

1 0

1 >=

1 55

1

1

0

0

-1

Constraint 6 -1

1 0

0 0

0 0

1 0

1 >=

1 60

1

1

1

0

-1

Constraint 7 -1

1 -1

0 0

0 0

1 0

1 >=

1 51

1

1

1

1

-1

Constraint 8 -1

1 -1

0 -1

0 0

1 0

1 <=

1 29

1

1

1

1

-1

Constraint 9 -1

0 -1

1 -1

0 -1

1 0

1 >=

1 14

1

1

1

1

-1

Constraint 10 0 -1 -1

0 -1

1 -1

1 -1

1 >=

1 9

1

1

1

1

-1

Constraint 11 0 -5 -4

0 -3

0 -2

10 -1

9 <=

8 7 128.4

6

5

4

-6

Dual Problem

Constraint 1 Constraint 7

Maximize

14

Constraint 2 Constraint 8

Constraint 3 Constraint 9

Constraint 4 Constraint 5 Constraint 6 Constraint 10 Constraint 11

25

26

38

55

60

51

-29

14

9

-128.4

F

1 1 80.88

0.5

0.5

1

1

1

-1

0

0

0

<=

F1

0 8.08

0

0

0

0

0

0

0

1

0

0

<=

F2

0 8.08

0

0

0

0

0

0

0

0

1

0

<=

P1

1 78.2

1

1

1

1

1

1

-1

1

1

-10

<=

P2

0 1 70.38

1

1

1

1

1

-1

1

1

-9

<=

P3

0 0 62.56

1

1

1

1

1

-1

1

1

-8

<=

P4

0 0 54.74

0

1

1

1

1

-1

1

1

-7

<=

P5

0 0 46.92

0

0

1

1

1

-1

1

1

-6

<=

P6

0 39.1

0

0

0

0

1

1

-1

1

1

-5

<=

P7

0 0 31.28

0

0

0

0

1

-1

1

1

-4

<=

Q4

0 0 46.92

0

0

-1

-1

-1

1

-1

-1

6

<=

Q5

0 39.1

0

0

0

0

-1

-1

1

-1

-1

5

<=

Q6

0 0 31.28

0

0

0

0

-1

1

-1

-1

4

<=

Q7

0 0 23.46

0

0

0

0

0

1

-1

-1

3

<=

Q8

0 0 15.64

0

0

0

0

0

0

-1

-1

2

<=

Q9

0 7.82

0

0

0

0

0

0

0

-1

1

<=

0

RANGING

Variable F

Value Reduced Cost Original Val

28.2286

0

80.88 38.58 93.32

Lower Bound Upper Bound

F1

13.2286

0

8.08

0

F2

8.2286 0

8.08

0

20.52

P1

0

27.7257

78.2

50.4743

Infinity

P2

0

13.8629

70.38 56.5172

Infinity

P3

11.8857

0

62.56 47.6308

75.4987

P4

12

0

54.74 40.8771

68.6029

P5

2.8857 0

46.92 31.9908

59.8587

P6

5

0

39.1

52.9629

P7

0

60.7829

Q4

0

93.84 46.92 -46.92 Infinity

Q5

0

78.2

Q6

0

1.7771 31.28 29.5029

Q7

31

0

Q8

0

19.7143

15.64 -4.0743

Q9

0

9.8571 7.82

-2.0371

Constraint

Dual Value

Slack/Surplus Original Val

Constraint 1

0

14.2286

14

Constraint 2

0

3.2286 25

-Infinity

28.2286

Constraint 3

-13.8629

0

26

13.2

38

Constraint 4

-13.8629

0

38

26

40.6933

Constraint 5

-13.8629

0

55

51.8923

Constraint 6

-74.6457

0

60

55

Constraint 7

0

51

-Infinity

Constraint 8

21.4914

0

29

21.4667

Constraint 9

-8.08

14

.7714

Infinity

39.1

-35.5457

20.52

31.28 -29.5029

-39.1

Infinity

Infinity Infinity

23.46 1.9686 25.2371

9

0

Infinity

Infinity

-Infinity

Lower Bound Upper Bound 28.2286

60

80.2 60 42.4667

Constraint 10 -8.08

0

Constraint 11 6.0429 0

9

.7714

128.4 88

Infinity 151