4 Jamil is building a summerhouse in his garden. The activities involved, the duration, immediate predecessors and number of workers required for each activity are listed in the table.
| Activity | Duration (hours) | Immediate predecessors | Number of workers |
| \(A\) : Choose summerhouse | 2 | - | 2 |
| \(B\) : Buy slabs for base | 1 | - | 2 |
| \(C\) : Take goods home | 2 | \(A , B\) | 2 |
| \(D\) : Level ground | 3 | - | 1 |
| E: Lay slabs | 2 | \(C , D\) | 2 |
| \(F\) : Treat wood | 3 | C | 1 |
| \(G\) : Install floor, walls and roof | 4 | \(E , F\) | 2 |
| \(H\) : Fit windows and door | 2 | \(G\) | 1 |
| \(I\) : Fit patio rail | 1 | \(G\) | 1 |
| \(J\) : Fit shelving | 1 | \(G\) | 1 |
- 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 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.
- Describe how it is possible for the project to be completed in the minimum project completion time when only four workers are available.
- Describe how two workers can complete the project as quickly as possible. Find the minimum time in which two workers can complete the project.