A project has the following activities: A(5 days), B(8 days), C(6 days), D(4 days). Activity B starts after A, C starts after A, and D starts after both B and C are complete. What is the total project duration?
Correct Answer
B) 17 days
Path 1: A(5) + B(8) + D(4) = 17 days. Path 2: A(5) + C(6) + D(4) = 15 days. The longest path determines project duration: 17 days.
Why This Is the Correct Answer
The critical path method requires identifying all possible paths and selecting the longest duration. Path 1: A(5) → B(8) → D(4) = 17 days. Path 2: A(5) → C(6) → D(4) = 15 days. Since D cannot start until both B and C are complete, the project duration is determined by the longest path, which is 17 days through activities A-B-D.
Why the Other Options Are Wrong
Option A: 19 days
19 days incorrectly assumes activities run sequentially without considering parallel execution. This would be A+B+C+D, but C runs parallel to B after A completes, not sequentially after B.
Option C: 23 days
23 days represents the sum of all activity durations (5+8+6+4), ignoring that some activities can run in parallel. This approach fails to recognize the network logic and parallel paths.
Option D: 21 days
21 days might result from incorrectly calculating parallel activities or misunderstanding the precedence relationships. This doesn't match either valid path calculation through the project network.
Memory Technique
Remember 'Longest Path Wins' - in project scheduling, the critical path (longest duration path) determines total project time, not the sum of all activities.
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