GATE 2026 ME – Question 65
The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic ($t_o$), most likely ($t_m$), and pessimistic ($t_p$) are given in the table below.
| Activity | $t_o$ | $t_m$ | $t_p$ |
|---|---|---|---|
| 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 |
The expected project length is ________ weeks (*in integer*).
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Show answer and explanation
Correct answer: 22
Explanation
The expected time of each activity is $\frac{t_o + 4t_m + t_p}{6}$. This gives 1-2: 5, 1-3: 4, 1-4: 5, 2-5: 6, 3-4: 6, 3-5: 3, 4-5: 7 and 5-6: 5. The paths to the end are 1-2-5-6 with $5 + 6 + 5 = 16$, 1-3-5-6 with 12, 1-4-5-6 with 17, and 1-3-4-5-6 with $4 + 6 + 7 + 5 = 22$. The longest path sets the project length, which is 22 weeks.