Chase Manhattan Bank
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Transcript of Chase Manhattan Bank
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EXTRA RICE
Objective Function : Minimize
Z_= 8(10.11)F+ 8.08(F1 + F2) + 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
F1 + P1 + P2 + P3 + P4 + P5 + P6+P7 - Q4 - Q5 - Q6 - Q7 - Q8 14
F2 + 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 + F2 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
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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 F1 F2 P1 P2 P3 P4 P5 P6 P7 Q4 Q5
Q6 Q7 Q8 Q9 RHS Dual
Minimize 80.88 8.08 8.08 78.2 70.38 62.56 54.74 46.92 39.1 31.28 46.92
39.1 31.28 23.46 15.64 7.82
Constraint 1 1 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 >= 14 0
Constraint 2 1 0 0 1 1 0 0 0 0 0 0
0 0 0 0 0 >= 25 0
Constraint 3 .5 0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 >= 26 -13.8629
Constraint 4 .5 0 0 1 1 1 1 0 0 0 0
0 0 0 0 0 >= 38 -13.8629
Constraint 5 1 0 0 1 1 1 1 1 0 0 -1
0 0 0 0 0 >= 55 -13.8629
Constraint 6 1 0 0 1 1 1 1 1 1 0 -1
-1 0 0 0 0 >= 60 -74.6457
Constraint 7 1 0 0 1 1 1 1 1 1 1 -1
-1 -1 0 0 0 >= 51 0
Constraint 8 1 0 0 1 1 1 1 1 1 1 -1
-1 -1 -1 0 0
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Constraint 9 0 1 0 1 1 1 1 1 1 1 -1
-1 -1 -1 -1 0 >= 14 -8.08
Constraint 10 0 0 1 1 1 1 1 1 1 1 -1
-1 -1 -1 -1 -1 >= 9 -8.08
Constraint 11 0 0 0 10 9 8 7 6 5 4 -6
-5 -4 -3 -2 -1 28.2286 13.2286 8.2286 0 0 11.8857 12 2.8857
5 0 0 0 0 31 0 0 4915.108
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
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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 F F1 F2 P1 P2 P3 P4 P5 P6 P7 Q4Q5 Q6 Q7 Q8 Q9
Constraint 1 1 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 >= 14
Constraint 2 1 0 0 1 1 0 0 0 0 0 0
0 0 0 0 0 >= 25
Constraint 3 0.5 0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 >= 26
Constraint 4 0.5 0 0 1 1 1 1 0 0 0 0
0 0 0 0 0 >= 38
Constraint 5 1 0 0 1 1 1 1 1 0 0 -1
0 0 0 0 0 >= 55
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Constraint 6 1 0 0 1 1 1 1 1 1 0 -1
-1 0 0 0 0 >= 60
Constraint 7 1 0 0 1 1 1 1 1 1 1 -1
-1 -1 0 0 0 >= 51
Constraint 8 1 0 0 1 1 1 1 1 1 1 -1
-1 -1 -1 0 0 = 14
Constraint 10 0 0 1 1 1 1 1 1 1 1 -1
-1 -1 -1 -1 -1 >= 9
Constraint 11 0 0 0 10 9 8 7 6 5 4 -6
-5 -4 -3 -2 -1
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P2 0 1 1 1 1 1 1 -1 1 1 -9
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F1 13.2286 0 8.08 0 20.52
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 -35.5457 52.9629
P7 0 60.7829 31.28 -29.5029 Infinity
Q4 0 93.84 46.92 -46.92 Infinity
Q5 0 78.2 39.1 -39.1 Infinity
Q6 0 1.7771 31.28 29.5029 Infinity
Q7 31 0 23.46 1.9686 25.2371
Q8 0 19.7143 15.64 -4.0743 Infinity
Q9 0 9.8571 7.82 -2.0371 Infinity
Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound
Constraint 1 0 14.2286 14 -Infinity 28.2286
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 60
Constraint 6 -74.6457 0 60 55 80.2
Constraint 7 0 9 51 -Infinity 60
Constraint 8 21.4914 0 29 21.4667 42.4667
Constraint 9 -8.08 0 14 .7714 Infinity
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Constraint 10 -8.08 0 9 .7714 Infinity
Constraint 11 6.0429 0 128.4 88 151
