GATE ME 2026 Set 1 — Question 65
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Question
The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic (), most likely (), and pessimistic () are given in the table below.
The expected project length is ________ weeks (in integer).
| Activity | |||
|---|---|---|---|
| 1−2 | 2 | 4 | 12 |
| 1−3 | 2 | 4 | 6 |
| 1−4 | 3 | 4 | 11 |
| 2−5 | 3 | 6 | 9 |
| 3−4 | 2 | 5 | 14 |
| 3−5 | 3 | 3 | 3 |
| 4−5 | 3 | 6 | 15 |
| 5−6 | 2 | 5 | 8 |
Correct answer
22 to 22
Solution
First, we calculate the expected time () for each activity using the formula :
- weeks
- weeks
- weeks
- weeks
- weeks
- weeks
- weeks
- weeks
1.Path 1-2-5-6: weeks
2.Path 1-3-5-6: weeks
3.Path 1-3-4-5-6: weeks
4.Path 1-4-5-6: weeks
The critical path is the longest path, which is 1-3-4-5-6 with a duration of 22 weeks. Therefore, the expected project length is 22 weeks.Continue learning with Success Tracker
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