1
2
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5
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7
8
9
A B C D E F
Activity 1 Activity 2
Unit Profit -1 1
Used Available
Resource A 2 -1 0<= 20
Resource B 1 -2 0<= 20
Activity 1 Activity 2 Total Profit
Number of Units
0 0 0
Resource Used Per Unit
1
2
3
4
5
6
7
8
9
10
A B C D E F
Activity 1 Activity 2
Unit Profit 2 1 ($million)
Used Available
Resource A 3 1 15 <= 15
Resource B 1 2 10 <= 10
Total Profit
Activity 1 Activity 2 ($million)
Number of Units
4 3 11
Resource Used Per Unit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F
Interior Point Algorithm for Problem 14.28c
Iteration x1x2Z
01.00000 1.00000 4.0000
11.87500 1.12500 6.7500
22.69810 0.80190 8.8962
33.34396 0.40095 10.4328
43.66710 0.20047 11.2018
53.83305 0.10024 11.5994
63.91648 0.05012 11.7996
73.95824 0.02506 11.8998
83.97912 0.01253 11.9499
93.98956 0.00626 11.9749
10 3.99478 0.00313 11.9875
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7
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9
10
11
12
13
14
A B C D E F
Interior Point Algorithm for Problem 14.29d
Iteration x1x2Z
01.00000 1.00000 2.0000
12.00000 2.00000 4.0000
22.50000 2.50000 5.0000
32.75000 2.75000 5.5000
42.87500 2.87500 5.7500
52.93750 2.93750 5.8750
62.96875 2.96875 5.9375
72.98437 2.98437 5.9688
82.99219 2.99219 5.9844
92.99609 2.99609 5.9922
10 2.99805 2.99805 5.9961
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7
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9
10
11
12
13
14
A B C D E F
Interior Point Algorithm for Problem 14.29e
Iteration x1x2Z
03.00000 1.00000 4.0000
13.38066 1.23867 4.6193
23.33770 1.82460 5.1623
33.07911 2.45717 5.5363
42.96654 2.76509 5.7316
52.94424 2.90206 5.8463
62.96055 2.95681 5.9174
72.97907 2.97901 5.9581
82.98952 2.98952 5.9790
92.99476 2.99476 5.9895
10 2.99738 2.99738 5.9948
Activity 1 Activity 2 Activity 3
Unit Profit 2 5 7
Resource Used Per Unit Used Available
Resource 1 2 3 6 <= 6
Activity 1 Activity 2 Activity 3 Total Profit
Number of Units 0 3 0 15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F
Interior Point Algorithm for Problem 14.30b
Iteration x1x2x3Z
01.00000 1.00000 1.00000 14.0000
10.50000 1.40000 0.90000 14.3000
20.25969 2.19516 0.45000 14.6452
30.17947 2.57276 0.22500 14.7978
40.10690 2.77780 0.11250 14.8903
50.05595 2.88765 0.05625 14.9439
60.02810 2.94376 0.02812 14.9719
70.01406 2.97188 0.01406 14.9859
80.00703 2.98594 0.00703 14.9930
90.00352 2.99297 0.00352 14.9965
10 0.00176 2.99648 0.00176 14.9982
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A B C D E F G H
Activity 1 Activity 2 Activity 3 Activity 4
Unit Profit 50 60 40 30
Used Available
Resource A 3 5 2 3 130 <= 130
Resource B 4 3 5 1 130 <= 130
Resource C 2 6 4 7 118.18 <= 190
Activity 1 Activity 2 Activity 3 Activity 4 Total Profit
Number of Units 23.64 11.82 0 0 1890.91
Resource Used Per Unit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G
Interior Point Algorithm for Problem 14.31b
Iteration x1x2x3x4Z
05.0000 6.0000 4.00000 3.00000 860.00
17.7865 10.4121 5.15582 3.42273 1322.97
29.6707 12.6928 5.25147 3.34029 1555.37
311.6525 13.3676 5.08441 3.17856 1683.41
414.2623 12.9152 4.64514 3.03224 1764.80
517.4541 11.9087 3.51576 2.90497 1815.01
620.9150 10.8139 1.83662 2.72815 1849.90
722.6670 10.3784 0.91831 2.48589 1867.37
823.4697 10.3745 0.45916 2.11734 1877.84
923.7466 10.6603 0.22958 1.59018 1883.84
10 23.7621 11.0802 0.11479 0.98935 1887.19
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A B C D E F G
X1 X2 X3
Unit Profit 4 3 6
Resource Used Per Unit Used Available
Constraint 1 3 1 3 30 <= 30
Constraint 2 2 2 3 40 <= 40
X1 X2 X3 Total Profit
Number of Units
010 6.667 70
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2
3
4
5
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7
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9
10
A B C D E F G
X1 X2 X3
Unit Profit 1 2 2
Resource Used Per Unit Used Available
Constraint 1 5 2 3 15 <= 15
Constraint 2 1 4 2 12 <= 12
Constraint 3 2 0 1 4.5 <= 8
X1 X2 X3 Total Profit
Number of Units
00.75 4.5 10.5