In an arrow diagram with nodes ① to ⑥, the activities, written as 'name: start node → end node, duration', are A: ① → ②, 6 days; B: ① → ③, 4 days; C: ② → ④, 4 days; D: ③ → ⑤, 4 days; E: ④ → ⑥, 2 days; F: ⑤ → ⑥, 3 days; and a dummy activity: ② → ③ (duration 0). What is the shortest duration of the whole project?

Answer: C. 13 days

The dummy activity ② → ③ means that activity D cannot start until A, as well as B, has finished. The earliest event times are 6 days at ②, max(4, 6 + 0) = 6 days at ③, 6 + 4 = 10 days at ④, 6 + 4 = 10 days at ⑤ and max(10 + 2, 10 + 3) = 13 days at ⑥, so the whole project takes 13 days and the critical path is A → dummy → D → F. Overlooking the dummy activity would let D start on day 4, making A → C → E, at 12 days, the longest path. 11 days is the length of the B → D → F path alone.

• A. This is only B → D → F (4 + 4 + 3), ignoring that A must also finish before D.
• B. This is the result of overlooking the dummy activity, which makes A → C → E (6 + 4 + 2) the longest.
• C. Correct. A → dummy → D → F, 6 + 0 + 4 + 3 = 13 days, is the longest path.