GATE ME 2019 Set 2 — Question 45
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Industrial Engineering → Operations Research → PERT & CPM
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Question
The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship "" means that is predecessor of activities and . The time to complete the activities along the critical path is ______ weeks.
| Activity | Duration (Weeks) | Precedence Relationship |
|---|---|---|
| A | 5 | A < B, C, D |
| B | 7 | B < E, F, G |
| C | 10 | C < I |
| D | 6 | D < G |
| E | 3 | E < H |
| F | 9 | F < I |
| G | 7 | G < I |
| H | 4 | H < I |
| I | 2 | ---- |
Correct answer
(C) 23
Solution
To find the critical path, we calculate the total duration for all possible paths from the start (Activity A) to the end (Activity I):
1.Path A-B-E-H-I: weeks
2.Path A-B-F-I: weeks
3.Path A-B-G-I: weeks
4.Path A-C-I: weeks
5.Path A-D-G-I: weeks
The critical path is the longest path in the network. Comparing the durations, the longest path is A-B-F-I with a duration of 23 weeks.Continue learning with Success Tracker
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