3 The table lists the duration, immediate predecessors and number of workers required for each activity in a project.
| Activity | Duration (hours) | Immediate predecessors | Number of workers |
| \(A\) | 3 | - | 1 |
| \(B\) | 2 | - | 1 |
| C | 2 | \(A\) | 2 |
| \(D\) | 3 | \(A\), \(B\) | 2 |
| E | 3 | \(C\) | 3 |
| \(F\) | 3 | C, D | 3 |
| \(G\) | 2 | D | 3 |
| \(H\) | 5 | \(E , F\) | 1 |
| I | 4 | \(F , G\) | 2 |
- Represent the project by an activity network, using activity on arc. You should make your diagram quite large so that there is room for working.
- Carry out a forward pass and a backward pass through the activity network, showing the early event times and late event times clearly at the vertices of your network.
State the minimum project completion time and list the critical activities.
- Draw a resource histogram to show the number of workers required each hour when each activity begins at its earliest possible start time.
- Show how it is possible for the project to be completed in the minimum project completion time when only six workers are available.