A small project network has five activities. Activity A (3 days) and Activity B (6 days) both start the project. Activity C (8 days) follows A. Activity D (4 days) follows B. Activity E (5 days) starts only after both C and D finish, and E ends the project. Which path is the project's critical path?
- AA to C to E, with a total duration of 16 days Correct
- BB to D to E, with a total duration of 15 days
- CA to C to E, with a total duration of 11 days
- DB to D to E, with a total duration of 18 days
Why A is correct: The critical path is the longest continuous path through the network. A to C to E sums to 3 plus 8 plus 5, which is 16 days, longer than the only other path B to D to E at 15 days, so it sets the earliest project finish and its activities have zero total float.
Why B is wrong: B to D to E is the near-critical path at 15 days and carries only 1 day of total float. It is tempting because it starts with the longest single activity, B at 6 days, but a longer path exists, so it is not critical.
Why C is wrong: This correctly names the longest path but miscalculates its length, most likely by dropping activity E from the sum. The path A to C to E actually totals 16 days, not 11, so the duration stated here is wrong.
Why D is wrong: This selects the near-critical path and also overstates its length, probably by adding an activity that is not on it. B to D to E totals 15 days, and in any case it is not the longest path, so it is not the critical path.