A project has the following activities:

Activity                              Duration                           Predecessors
A                                          5                                          -
B                                          7                                          A
C                                          6                                          A
D                                          4                                          B, C
E                                          3                                          D

Using Critical Path Method (CPM), what is the total project duration?

Question

A project has the following activities:
 
Activity                              Duration                           Predecessors 
A                                          5                                          -
B                                          7                                          A            
C                                          6                                          A
D                                          4                                          B, C
E                                          3                                          D
 
Using Critical Path Method (CPM), what is the total project duration?

BlackTom AI · Accepted Answer

Critical path is the longest-duration sequence of dependent activities; here that sequence is A → B → D → E with total duration 5 + 7 + 4 + 3 = 19 days.

1. Relevant knowledge points and concepts
- Critical Path Method (CPM): the project duration equals the length of the longest path (in time) from start to finish through the activity network.
- Earliest Start (ES) and Earliest Finish (EF): EF = ES + duration. For activities with predecessors, ES = maximum EF of all immediate predecessors.
- Slack: difference between latest and earliest times; activities on the critical path have zero slack.

2. Step-by-step reasoning and network evaluation
- Activity A has no predecessors: ES_A = 0, EF_A = ES_A + dur_A = 0 + 5 = 5.
- Activity B predecessor A: ES_B = EF_A = 5, EF_B = 5 + 7 = 12.
- Activity C predecessor A: ES_C = EF_A = 5, EF_C = 5 + 6 = 11.
- Activity D predecessors B and C: ES_D = max(EF_B, EF_C) = max(12, 11) = 12, EF_D = 12 + 4 = 16.
- Activity E predecessor D: ES_E = EF_D = 16, EF_E = 16 + 3 = 19.

3. Intermediate calculations shown
- A: ES 0, EF 5
- B: ES 5, EF 12
- C: ES 5, EF 11
- D: ES 12, EF 16
- E: ES 16, EF 19

4. Why the correct answer is correct
The project cannot finish before the last activity (E) finishes. The EF of the final activity E is 19 days, which is set by the longest predecessor chain A → B → D → E (5 + 7 + 4 + 3 = 19). That longest path determines the project duration.

5. Why the other options are incorrect
- 16 Days and 17 Days are shorter than any of the full-path totals and ignore necessary successor durations.
- 18 Days corresponds to the alternative path A → C → D → E (5 + 6 + 4 + 3 = 18), which is shorter and therefore not the critical path; the project still requires the longer 19-day path.

6. Conclusion
The total project duration equals the critical path length, 19 Days, which matches the provided answer.

A project has the following activities: Activity Duration Predecessors A 5 - B 7 A C 6 A D 4 B, C E 3 D Using Critical Path Method (CPM), what is the total project duration?Single choice

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