ITPEC FE Morning April 2022 Question 55

26 days — the minimum completion time is the length of the longest path, the critical path A–E–G–I.

Earliest finish of each activity, starting each one when all activities before it are done:

• •A ends at 3, B at 8, C at 3 + 4 = 7, D at 3 + 7 = 10, E at 3 + 11 = 14
• •F starts after B and C: 8 + 7 = 15
• •G starts after E: 14 + 8 = 22
• •H starts after D, F and, through the dummy, E: 15 + 6 = 21
• •I starts after G and H: 22 + 4 = 26

Answer (d)

Why not others:

• •(a) 20 — the shortest path A–D–H–I; the project ends only when every activity is done, so the longest path decides
• •(b) 24 — A–E–dummy–H–I or A–C–F–H–I, paths with slack
• •(c) 25 — B–F–H–I, the longest path through H, but the E–G branch reaches the start of I one day later than H does

Key rule: "Minimum project duration" means the critical path, the longest path through the network; a dummy adds no time but still passes on a dependency.

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