A project has activities with the following durations: A(5 days), B(8 days), C(6 days), D(4 days). The network shows A and B can start immediately, C depends on A, and D depends on both B and C. What is the critical path duration?
Correct Answer
B) 15 days
Path 1: A→C→D = 5+6+4 = 15 days. Path 2: B→D = 8+4 = 12 days (but D can't start until both B and C are complete). The critical path is A→C→D at 15 days.
Why This Is the Correct Answer
The critical path is the longest sequence of dependent activities that determines the minimum project duration. Since D depends on both B and C completing, we must wait for both paths to finish before D can start. Path A→C takes 11 days (5+6), while B takes 8 days, so D starts after day 11. The total critical path A→C→D equals 5+6+4 = 15 days.
Why the Other Options Are Wrong
Option A: 13 days
13 days is too short and doesn't account for the full critical path sequence. This might result from incorrectly calculating just A+B (5+8) or missing the dependency relationships.
Option C: 17 days
17 days exceeds the actual critical path duration. This might result from incorrectly adding all activities together or misunderstanding the parallel nature of A and B.
Option D: 23 days
23 days would result from incorrectly adding all four activities in series (5+8+6+4), ignoring that A and B can run in parallel.
Memory Technique
Remember 'LONGEST PATH WINS' - the critical path is always the longest sequence of dependent activities that cannot be shortened without delaying the entire project.
Reference Hint
Look up 'Critical Path Method (CPM)' and 'Project Scheduling' in construction management chapters, typically found in project management or scheduling sections.
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