taylmod cff
Post on 24-Jul-2016
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4. a.
The rounded down solution would not beoptimal.
3. a.
117.13
225
318
x1 ≥ 6x1 ≤ 5 11,473
21,460
31,460
x1 ≥ 24x1 ≤ 23
Relaxed solution: x1 = 10.8, x2 = 23, s1 = 2.6
b. Relaxed solution: x1 = 6, x2 = 3.2, s2 = 4.8,Z = 2,720
Relaxed solution: x1 = 10, x2 = 24.5, s2 = 4
2. Relaxed solution: x1 = 5.71, Z = 17.13 b. Relaxed solution: x1 = 10.5, x2 = 23.7, Z = 1,473
x1 = 5, x2 = 1.67, Z = 25
x1 = 6, s1 = 2, Z = 18
12,720
22,700
32,400
x1 ≥ 4x1 ≤ 3
Relaxed solution: x1 = 6, x2 = 3, s1 = 2, s2 = 6,Z = 2,700
Relaxed solution: x1 = 5, x2 = 4, s2 = 2, s3 = 1,Z = 2,400
5. a.
25
20
15
10
5
0 5 10 15 20 25 30x1
x2Node 1:
x1 = 6.25 x2 = 0
Relaxed solution: x1 = 6, x2 = 1, s1 = 8, Z = 310
Infeasible
b.
25
20
15
10
5
0 5 10 15 20 25x1
x2Node 2:
x1 = 6 x2 = 1
25
20
15
10
5
0 5 10 15 20 25x1
x2Node 3:
InfeasibleOptimal integersolution:
UB = 312.5 (x1 = 6.25, x2 = 0)LB = 300 (x1 = 6, x2 = 0)
1312.5
2310
3�
x1 ≥ 7x1 ≤ 6
UB = 310 (x1 = 6, x2 = 1)LB = 310 (x1 = 6, x2 = 1)
InfeasibleOptimal solution at node 2:
x1 = 6x2 = 1Z = 310
6. a.
Relaxed solution: x2 = 10.71, s2 = 1.28, s2 = 5,Z = 5,785.7
Relaxed solution: x1 = 0.63, x2 = 10, s1 = 1.39, s2 = 4.37,Z = 5,778
15,785.7
25,778
3�
x2 ≥ 11x2 ≤ 10
Relaxed solution: x1 = 0, x2 = 10, x3 = 1, s1 = 1,s2 = 5, Z = 5,775
7. a.
15,767.8
15,785.7
25,778
3�
x2 ≥ 11
x1 ≥ 1
x2 ≤ 10
x1 = 0
45,775
Infeasible
Relaxed solution: x1 = 1, x2 = 9.57, s1 = 1.43, s2 = 4,s4 = .43, Z = 5,767.8
5
1372.9
2366.5
3365.0
x2 ≥ 6x2 ≤ 5
Relaxed solution: x1 = 3.33, x2 = 5, s1 = 3.33,Z = 366.5
Relaxed solution: x1 = 2.5, x2 = 6, s2 = 0.5,Z = 365
1360.0
1372.9
2366.5
3365.0
x2 ≥ 6
x1 ≥ 4
x2 ≤ 5
x1 = 3
4350.0
Relaxed solution: x1 = 3, x2 = 5, s1 = 4, s2 = 1,Z = 350
Relaxed solution: x1 = 4, x2 = 4, s1 = 7, s3 = 1,Z = 360
5
The rounded down solution would not beoptimal.
5360.0
1372.9
2366.5
3365.0
x2 ≥ 6
x1 ≥ 4
x2 ≤ 5
x1 = 3 x1 ≥ 3x1 = 2
4350.0
7�
6350.0 Infeasible
Relaxed solution: x1 = 2, x2 = 6.25, s2 = 0.5, s3 = 0.25,Z = 350
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