A project has the following activities: A(4 days) → B(6 days) → D(3 days) and A(4 days) → C(8 days) → D(3 days). Activity D cannot start until both B and C are complete. What is the critical path duration?
Correct Answer
B) 15 days
Path 1: A(4) + B(6) + D(3) = 13 days. Path 2: A(4) + C(8) + D(3) = 15 days. The critical path is the longest path, which is 15 days through A-C-D.
Why This Is the Correct Answer
The critical path is the longest sequence of activities that determines the minimum project duration. In this network, there are two possible paths from start to finish: A-B-D (13 days) and A-C-D (15 days). Since Activity D cannot start until both B and C are complete, we must wait for the longer path (A-C-D) to finish before D can begin. Therefore, the critical path duration is 15 days.
Why the Other Options Are Wrong
Option A: 19 days
17 days is incorrect as it doesn't correspond to any valid path calculation in this network. The longest path A-C-D only totals 15 days (4+8+3), not 17 days.
Option C: 17 days
13 days represents only the duration of path A-B-D, but this ignores the constraint that Activity D cannot start until both B and C are complete. Since path A-C-D takes 15 days, D cannot actually start after only 13 days.
Memory Technique
Remember 'LONGEST = CRITICAL' - the critical path is always the longest duration path through your project network, as it controls when your project can finish.
Reference Hint
Look up 'Critical Path Method (CPM)' and 'Project Scheduling' in construction management chapters, typically found in project management or scheduling sections of contractor reference materials.
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