Consider a project with 4 activities. The project network is shown below:

Activity Duration (weeks)
A 3
B 5
C 4
D 1

What is the earliest completion time of the project?

Question

Consider a project with 4 activities. The project network is shown below:

Activity    Duration (weeks)
A        3 
B        5 
C        4
D        1

What is the earliest completion time of the project?

BlackTom AI · Accepted Answer

The project’s earliest completion equals the length of the critical path (the longest path of dependent activities) through the network.

1) Relevant knowledge points and concepts
- In a project network with activity durations, perform a forward pass to compute earliest start (ES) and earliest finish (EF) times.
- EF = ES + duration. For nodes with multiple predecessors, ES = maximum of predecessor EFs.
- The earliest project completion time is the EF of the terminal activity (or the length of the longest path from start to finish).

2) Step-by-step reasoning (forward pass)
- Start time = 0.
- Activity A has no predecessors: ES_A = 0, EF_A = ES_A + dur_A = 0 + 3 = 3.
- Activity B follows A: ES_B = EF_A = 3, EF_B = ES_B + dur_B = 3 + 5 = 8.
- Activity C also follows A: ES_C = EF_A = 3, EF_C = ES_C + dur_C = 3 + 4 = 7.
- Activity D follows both B and C: ES_D = max(EF_B, EF_C) = max(8, 7) = 8, EF_D = ES_D + dur_D = 8 + 1 = 9.

3) All intermediate calculations shown
- EF_A = 0 + 3 = 3
- EF_B = 3 + 5 = 8
- EF_C = 3 + 4 = 7
- ES_D = max(8, 7) = 8 → EF_D = 8 + 1 = 9

4) Why the correct answer is correct
- The critical path is A → B → D with total duration 3 + 5 + 1 = 9 weeks. Activity D cannot finish until both predecessor paths complete; B finishes later than C, so the project completion is governed by the A-B-D path (9 weeks).

5) Why other options are incorrect (brief)
- 8 weeks: equals A → C → D (3 + 4 + 1 = 8) but is shorter than the critical path, so project cannot finish that early.
- 13 weeks: likely an incorrect sum of activities treated serially or double-counted; not supported by network dependencies.
- 3 weeks or 7 weeks: represent only single-path partial sums (A alone = 3; A + C = 7) and ignore remaining dependent activities.

6) Conclusion
- The earliest completion time is 9 weeks, which matches the provided correct answer.

Consider a project with 4 activities. The project network is shown below: Activity Duration (weeks) A 3 B 5 C 4 D 1 What is the earliest completion time of the project?单项选择题

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