Using the activity data below, identify the critical path and the total project duration.

Activity                       Duration (Days) Predecessors
A                                 4 -
B                                 2 A
C                                 4 A
D                                 2 B
E                                  5 B
F                                  3 D, E
G                                 2 F, C
H                                 3 G
I                                   4 E
J                                  2 H, I

Question

Using the activity data below, identify the critical path and the total project duration.

Activity                       Duration (Days)              Predecessors 
A                                 4                                       -
B                                 2                                       A         
C                                 4                                       A
D                                 2                                       B
E                                  5                                       B
F                                  3                                       D, E
G                                 2                                        F, C
H                                 3                                        G
I                                   4                                       E
J                                  2                                        H, I

BlackTom AI · Accepted Answer

Compute earliest-start (ES) and earliest-finish (EF) times via a forward pass:

1) Relevant concepts
- Critical path is the longest-duration sequence of dependent activities from start to finish; its length equals project duration.
- Forward pass computes ES and EF (EF = ES + duration). For an activity with multiple predecessors, ES = max(EF of predecessors).
- Any path shorter than the critical path has slack and is not critical.

2) Forward-pass calculations (all times in days)
- A: ES = 0, EF = 0 + 4 = 4
- B: ES = EF(A) = 4, EF = 4 + 2 = 6
- C: ES = EF(A) = 4, EF = 4 + 4 = 8
- D: ES = EF(B) = 6, EF = 6 + 2 = 8
- E: ES = EF(B) = 6, EF = 6 + 5 = 11
- F: ES = max(EF(D)=8, EF(E)=11) = 11, EF = 11 + 3 = 14
- G: ES = max(EF(F)=14, EF(C)=8) = 14, EF = 14 + 2 = 16
- H: ES = EF(G) = 16, EF = 16 + 3 = 19
- I: ES = EF(E) = 11, EF = 11 + 4 = 15
- J: ES = max(EF(H)=19, EF(I)=15) = 19, EF = 19 + 2 = 21

3) Path duration checks (sum of activity durations along each path)
- Path A–B–E–F–G–H–J: 4 + 2 + 5 + 3 + 2 + 3 + 2 = 21 days
- Path A–C–G–H–J: 4 + 4 + 2 + 3 + 2 = 15 days
- Path A–B–D–F–G–H–J: 4 + 2 + 2 + 3 + 2 + 3 + 2 = 18 days
- Path A–B–E–I–J: 4 + 2 + 5 + 4 + 2 = 17 days

4) Why the correct answer is correct
The longest path (critical path) is A–B–E–F–G–H–J with total duration 21 days. This matches the forward-pass EF for the final activity J (21), so no other path can extend the project beyond 21 days.

5) Why other options are incorrect
- Option 2 (A–C–G–H–J; 19 days): the computed sum for that path is 15 days, not 19, and it’s shorter than 21.
- Option 3 (A–B–D–F–G–H–J; 20 days): that path sums to 18 days, not 20, and is shorter than 21.
- Option 4 (A–B–E–I–J; 17 days): this path sums to 17 days and finishes at time 17, so it cannot be critical.

6) Conclusion
The critical path is A – B – E – F – G – H – J and the total project duration is 21 days, which matches the provided correct answer.

Using the activity data below, identify the critical path and the total project duration. Activity Duration (Days) Predecessors A 4 - B 2 A C 4 A D 2 B E 5 B F 3 D, E G 2 F, C H 3 G I 4 E J 2 H, I 单项选择题

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