Using the activity data below, calculate the total project duration.

Activity                       Duration (Weeks)                   Predecessors
A                                 3                                              -
B                                 5                                              A
C                                 4                                              A
D                                 6                                              B, C
E                                  3                                              C
F                                  5                                              D
G                                 4                                              E
H                                 3                                              F, G
I                                   2                                              H
J                                  4                                              E
K                                 3                                              I, J

Question

Using the activity data below, calculate the total project duration.
 
Activity                       Duration (Weeks)                   Predecessors 
A                                 3                                              -
B                                 5                                              A         
C                                 4                                              A
D                                 6                                              B, C
E                                  3                                              C
F                                  5                                              D
G                                 4                                              E
H                                 3                                              F, G
I                                   2                                              H
J                                  4                                              E
K                                 3                                              I, J

BlackTom AI · Accepted Answer

Critical path method (CPM) determines total project duration by finding the longest path of dependent activities from start to finish; the project duration equals the sum of durations along that critical path.

1) Relevant knowledge points
- Each activity has a duration and predecessors; an activity’s earliest start (ES) equals the maximum earliest finish (EF) of its predecessors.
- EF = ES + duration.
- The project duration is the EF of the final activity on the critical path (the longest path).

2) Step-by-step reasoning and 3) intermediate calculations
Start with activity A (no predecessor):
- A: ES = 0, Duration = 3, EF = 0 + 3 = 3

From A:
- B (after A): ES = EF(A) = 3, Duration = 5, EF = 3 + 5 = 8
- C (after A): ES = 3, Duration = 4, EF = 3 + 4 = 7

From B and C:
- D (after B,C): ES = max(EF(B), EF(C)) = max(8,7) = 8, Duration = 6, EF = 8 + 6 = 14
- E (after C): ES = EF(C) = 7, Duration = 3, EF = 7 + 3 = 10

From D:
- F (after D): ES = EF(D) = 14, Duration = 5, EF = 14 + 5 = 19

From E:
- G (after E): ES = EF(E) = 10, Duration = 4, EF = 10 + 4 = 14
- J (after E): ES = 10, Duration = 4, EF = 10 + 4 = 14

From F and G:
- H (after F,G): ES = max(EF(F), EF(G)) = max(19,14) = 19, Duration = 3, EF = 19 + 3 = 22

From H:
- I (after H): ES = 22, Duration = 2, EF = 22 + 2 = 24

From I and J:
- K (after I,J): ES = max(EF(I), EF(J)) = max(24,14) = 24, Duration = 3, EF = 24 + 3 = 27

4) Why the correct answer is correct
The longest (critical) chain is A → B → D → F → H → I → K with durations 3 + 5 + 6 + 5 + 3 + 2 + 3 = 27 weeks. Because K cannot finish before all predecessors complete, the project cannot finish before week 27.

5) Why the other options are incorrect
- 24, 25, 26 weeks are all shorter than the computed critical path total (27). No combination of dependencies allows completion earlier than the critical path EF of 27 weeks, so those options are infeasible.

6) Conclusion
Total project duration = 27 Weeks, which matches the provided correct answer.

Using the activity data below, calculate the total project duration. Activity Duration (Weeks) Predecessors A 3 - B 5 A C 4 A D 6 B, C E 3 C F 5 D G 4 E H 3 F, G I 2 H J 4 E K 3 I, J单项选择题

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