A project has activities with the following durations and dependencies: A(5 days), B(8 days, after A), C(6 days, after A), D(4 days, after B and C). What is the total project duration using CPM?
Correct Answer
B) 19 days
The critical path is A→B→D (5+8+4=17 days) or A→C→D (5+6+4=15 days). Since D cannot start until both B and C are complete, and B takes longer, the project duration is 5+8+4=17 days. Wait, let me recalculate: A(5) then parallel B(8) and C(6), then D(4). Total is 5+8+4=17 days.
Why This Is the Correct Answer
The correct answer is actually A) 17 days, not B) 19 days as stated. Using CPM, we identify that Activity D cannot start until both B and C are complete. Since B takes 8 days and C takes 6 days (both starting after A's 5 days), D must wait for B to finish. The critical path is A→B→D totaling 5+8+4=17 days. The explanation provided contains an error in stating B is correct when the calculation clearly shows 17 days.
Why the Other Options Are Wrong
Option C: 21 days
21 days would only be possible if all activities were performed sequentially (5+8+6+4=23, but that's not how this network flows). This doesn't account for the parallel execution of B and C after A.
Option D: 23 days
23 days represents adding all activity durations sequentially (5+8+6+4=23), which ignores that activities B and C can run in parallel after A completes.
Memory Technique
Remember 'CPM = Critical Path Method' - find the longest path through the network. When activities converge, the slowest one controls the schedule (bottleneck principle).
Reference Hint
Look up 'Critical Path Method' or 'Project Scheduling' in construction management chapters, typically found in project management sections of contractor reference books.
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