Hw Prob 9.26_grp4

Group 4: Megan Delay, Gary Conway, Andrew Detmers, Abby Detmers Chapter 9 Homework #26 a, b) Time Immediate Activity Required Predecessors ES EF LS A 4 0 4 0 B 2 A 4 6 4 C 3 B 6 9 9 D 1 C 9 10 12 E 1 D 10 11 13 F 2 B 6 8 8 G 3 F 8 11 10 H 1 G 11 12 13 I 5 B 6 11 6 J 3 I 11 14 11 K 4 C,F,I 14 18 14 L 2 K 18 20 18 M 1 L 20 21 20

1

2 A 4

B2

3

D1

4

C3 F2

I5

LF 4 6 12 13 14 10 13 14 11 14 18 20 21

7

G3

5

6

Slack 0 0 3 3 3 2 2 2 0 0 0 0 0

8

E1 H1

10

9 K4

11 L2

12 M1

J3

Critical Path = A-B-I-J-K-L-M = 21 Weeks d)

No, the project will not necessarily be delayed as a result of the failed air compressor because both Activity G and Activity H have a slack time of 2 weeks and neither activity is on the critical path.

e)

Activities: A,B,C,D,E,F,G,H,I,J must be completed by the end of week 15 to guarantee that the project is not delayed because all of these activities have LF times less than or equal to 15 weeks.

Group 4: Megan Delay, Gary Conway, Andrew Detmers, Abby Detmers Chapter 9 Homework #26 c) Gantt Chart A B C D E F G H I J K L M

Slack Slack Slack Slack Slack Slack

5

10

15

20

Variables Values

Constraints A B C D E F G H I J K L M

X1 0

-1

X2 4

1 -1

X3 6

1 -1

X4 9

X5 8

1 -1

-1

-1

Objective Function = min ∑xi from i=1 to 12 subject to the following constraints: x2 - x1 ≥ 4 x3 - x2 ≥ 2 x4 - x3 ≥ 3 x7 - x4 ≥ 1 x9 - x7 ≥ 1 x5 - x3 ≥ 2 x8 - x5 ≥ 3 x9 - x8 ≥ 1 x6 - x3 ≥ 5 x9 - x6 ≥ 3 x10 - x9 ≥ 4 x11 - x10 ≥ 2 x12 - x11 ≥ 1 xi ≥ 0 for 1 ≤ xi ≤ 12

X6 11

X7 10

X8 11

1 -1 1 -1

X10 18

X11 20

X12 21

Obj Func. 132

1 1 -1

1 -1

X9 14

1 1 -1

1 -1

1 -1

1

4 2 3 1 4 2 3 3 5 3 4 2 1

≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥

4 2 3 1 1 2 3 1 5 3 4 2 1