5 The table shows some of the activities involved in building a block of flats. The table gives their durations and their immediate predecessors.
| Activity | Duration (weeks) | Immediate Predecessors |
| A | Survey sites | 8 | - |
| B | Purchase land | 22 | A |
| C | Supply materials | 10 | - |
| D | Supply machinery | 4 | - |
| E | Excavate foundations | 9 | B, D |
| F | Lay drains | 11 | B, C, D |
| G | Build walls | 9 | E, F |
| H | Lay floor | 10 | E, F |
| I | Install roof | 3 | G |
| J | Install electrics | 5 | G |
- Draw an activity on arc network for these activities.
- Mark on your diagram the early and late times for each event. Give the minimum completion time and the critical activities.
Each of the tasks E, F, H and J can be speeded up at extra cost. The maximum number of weeks by which each task can be shortened, and the extra cost for each week that is saved, are shown in the table below.
| Task | E | F | H | J |
| Maximum number of weeks by | | which task may be shortened |
| 3 | 3 | 1 | 3 |
| Cost per week of shortening task | | (in thousands of pounds) |
| 30 | 15 | 6 | 20 |
- Find the new shortest time for the flats to be completed.
- List the activities which will need to be speeded up to achieve the shortest time found in part (iii), and the times by which each must be shortened.
- Find the total extra cost needed to achieve the new shortest time.