The GATE Grind

GATE 2019 ME (ME2) – Question 45

Operations Research · Network flow models, PERT and CPM · 2 marks · Multiple choice

Activities, durations (weeks) and immediate successors are: A: 5, B/C/D; B: 7, E/F/G; C: 10, I; D: 6, G; E: 3, H; F: 9, I; G: 7, I; H: 4, I; I: 2, none. Here X < Y,Z means X precedes Y and Z. Find the critical-path duration (weeks).

  1. 17
  2. 21
  3. 23
  4. 25

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Correct answer: (C) 23

Explanation

Earliest finishes are A 5, B 12, C 15, D 11, E 15, F 21, G 19 and H 19. I starts at $\max(15,21,19,19)=21$ and ends at 23. Critical path is A→B→F→I, duration $5+7+9+2=23$ weeks. **C**.