The table provides a project with the task lengths (in days) and precedence requ
ID: 432943 • Letter: T
Question
The table provides a project with the task lengths (in days) and precedence requirements, as well as the three time estimates. Task Length Predecessor Optimistic Most Likely Pessimistic A 7 — 6.1 7 7.5 B 4 A 2.5 4 6 C 8 A 6.7 8 8.75 D 3 B, C 2 3 4.5 E 2 B 1.5 2 2.3 F 8 D, E 7.3 8 8.7 Based on the information, which of the following statements is true? None of the paths in the project is a critical path. Path ABEF is the critical path for the project. Path ABDF is the critical path for the project. Path ACDF is the critical path for the project. Tasks A, B, C, D, and F lie in the critical path for the project.
Explanation / Answer
The precedence diagram of activities as follows :
A
B
C
E
D
F
Following table presents expected duration of each activity. It is to be noted that Expected duration of each activity = ( Optimistic + 4 x Most likely + Pessimistic) / 6
Task
Predecessor
Optimistic(O)
Most likely(M)
Pessimistic(P)
Expected Duration ( O + 4.M + P/6)
A
None
6.1
7
7.5
6.93
B
A
2.5
4
6
4.08
C
A
6.7
8
8.75
7.91
D
B,C
2
3
4.5
3.08
E
B
1.5
2
2.3
1.97
F
D,E
7.3
8
8.7
8.00
On basis of above precedence diagram and the table for expected durations of each activity . the possible parallel paths and their corresponding expected durations as follows :
A-B-E-F = 6.93 + 4.08 + 1.97 + 8 = 20.98
A-B-D-F = 6.93 + 4.08 + 3.08 + 8 = 22.09
A-C-D-F = 6.93 + 7.91 + 3.08 + 8 = 25.92
Out of above, since A-C-D-F has the longest duration, it is the critical path .
PATH A-C-D-F IS THE CRITICAL PATH FOR THE PROJECT
A
B
C
E
D
F
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