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Example solutions to Exercise Set 5

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Example solutions to Exercise Set 5

1. 1. Weighted, all decision variables binary, except tennis courts are integer 1 2 3 4 5 6 Golf 1 0 Swimming 0 0 0 1 Gymnasium 0 0 0 0 Tennis courts 1 1 2 2 45 45 90 119 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45
2. 2. Construction cost Maintenance cost User days 340 340 80 80 31 300 300 36 36 32 840 0 50 0 0 85 510 17 102 127 1150 218 190 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 50 1200 1200 1000 0 2 0 10 200 200 2 20 3 18 0 200 200 1 18 38
3. 3. Weighted, all decision variables binary 1 2 3 4 5 6 Golf 1 0 Swimming 0 0 1 1 Gymnasium 0 0 0 0 Tennis courts 0 1 1 1 0 45 74 74 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45
4. 4. Construction cost Maintenance cost User days 340 340 80 80 31 300 600 36 72 64 840 0 50 0 0 85 255 17 51 65 1195 203 160 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 5 1200 1200 1000 0 2 0 40 200 200 2 80 3 3 0 200 200 1 3 83
5. 5. Pre-emptive, Round 1, all decision variables binary, except tennis courts are integer 1 2 3 4 5 6 Golf 0 0 Swimming 1 0 0 1 Gymnasium 0 0 0 0 Tennis courts 0 1 1 2 29 45 45 119 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45 Note: There are multiple optimal solutions for Goal 1. This is what Excel gives if you start from all zeros.
6. 6. Construction cost Maintenance cost User days 340 0 80 0 0 300 600 36 72 58 840 0 50 0 0 85 340 17 68 85 940 140 143 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 260 1200 1200 1000 0 2 0 57 200 200 2 114 3 0 60 200 200 1 0 114 om all zeros.
7. 7. Pre-emptive, Round 2, all decision variables binary, except tennis courts are integer 1 2 3 4 5 6 Golf 0 0 Swimming 0 0 0 1 Gymnasium 0 0 0 0 Tennis courts 1 1 2 2 45 45 90 119 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45 Note: There are multiple optimal solutions for Goal 1. This is what Excel gives if you start from all zeros.
8. 8. Construction cost Maintenance cost User days 340 0 80 0 0 300 300 36 36 32 840 0 50 0 0 85 510 17 102 127 810 138 159 <= Goal 1, 1st round 940 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 390 1200 1200 1000 0 2 0 41 200 200 2 82 3 0 62 200 200 1 0 82 om all zeros.
9. 9. Pre-emptive, Round 1, all decision variables binary 1 2 3 4 5 6 Golf 0 0 Swimming 0 0 1 1 Gymnasium 0 0 0 0 Tennis courts 1 1 1 1 45 45 74 74 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45 Note: There are multiple optimal solutions for Goal 1. This is what Excel gives if you start from all zeros.
10. 10. Construction cost Maintenance cost User days 340 0 80 0 0 300 600 36 72 64 840 0 50 0 0 85 340 17 68 85 940 140 149 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 260 1200 1200 1000 0 2 0 51 200 200 2 102 3 0 60 200 200 1 0 102 om all zeros.
11. 11. Pre-emptive, Round 2, all decision variables binary 1 2 3 4 5 6 Golf 0 0 Swimming 0 0 1 1 Gymnasium 0 0 0 0 Tennis courts 1 1 1 1 45 45 74 74 <= <= <= <= Land requirement 70 80 95 120 User days 1 2 3 4 5 6 Golf 31 27 Swimming 26 21 32 32 Gymnasium 37 29 28 38 Tennis courts 20 23 22 20 Land requirement 1 2 3 4 5 6 Golf Swimming 29 29 29 29 Gymnasium 38 38 38 38 Tennis courts 45 45 45 45 Note: There are multiple optimal solutions for Goal 1. This is what Excel gives if you start from all zeros.
12. 12. Construction cost Maintenance cost User days 340 0 80 0 0 300 600 36 72 64 840 0 50 0 0 85 340 17 68 85 940 140 149 <= Goal 1, 1st round 940 Goal Over Under Goal LHS Goal RHS Weight Weighted sum 1 0 260 1200 1200 1000 0 2 0 51 200 200 2 102 3 0 60 200 200 1 0 102 om all zeros.
13. 13. x y x^2y xy^3 y^3 749.8703 1125.065 6.33E+08 1.07E+12 1.42E+09 2 3 2 3.21E+12 50 100 150000 <= 150000 Initial values Final values x0 y0 x y obj 0 0 0 0 0 1 1 749.8703 1125.065 3.21E+12 -1000 -1000 -1.8E+10 -5.4E+10 8.3E+42 1000 1000 749.8703 1125.065 3.21E+12
14. 14. x y x^2y xy^3 y^3 749.8703 1125.065 6.33E+08 1.07E+12 1.42E+09 2 3 2 3.21E+12 50 100 150000 <= 150000 Initial values Final values x0 y0 x y obj 0 0 0 0 0 1 1 749.8703 1125.065 3.21E+12 -1000 -1000 0 0 0 1000 1000 749.8703 1125.065 3.21E+12