Discussion
Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.
| Activity | Time (hours) | Immediate predecessors |
|---|---|---|
| A | 2 | - |
| B | 3 | - |
| C | 2 | - |
| D | 4 | A |
| E | 5 | B |
| F | 4 | B |
| G | 3 | C |
| H | 10 | D, E |
| I | 5 | F |
| J | 8 | G |
| K | 3 | H, I, J |
Answer: B
The latest finish time for G is 10 hours.
Forward pass (earliest finish): A 2, B 3, C 2; D 6, E 8, F 7, G 5; H starts after D and E, so finishes at 8 + 10 = 18; I 12; J 13; K starts after H, I and J, at 18, and finishes at 21. The project takes 21 hours along the critical path B-E-H-K.
Backward pass: K must finish by 21, so it starts by 18; J must therefore finish by 18 and start by \(18 - 8 = 10\). G is J's only predecessor, so G must finish by 10 hours.
5 is G's earliest finish, 8 confuses it with J's duration, and 9 has no basis. G has 5 hours of slack, so it is not critical.
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