6 Tariq wants to advertise his gardening services. The activities involved, their durations (in hours) and immediate predecessors are listed in the table.
| Activity | Duration (hours) | Immediate predecessors |
| A | Choose a name for the gardening service | 2 | - |
| B | Think about what the text needs to say | 3 | - |
| C | Arrange a photo shoot | 2 | B |
| D | Visit a leaflet designer | 3 | A, \(C\) |
| E | Design website | 5 | A, \(C\) |
| \(F\) | Get business cards printed | 3 | D |
| G | Identify places to publicise services | 2 | A, \(C\) |
| H | Arrange to go on local radio | 3 | B |
| I | Distribute leaflets | 4 | D, G |
| J | Get name put on van | 1 | E |
- Draw an activity network, using activity on arc, to represent the project.
- Carry out a forward pass and a backward pass through the activity network, showing the early event time and the late event time at each vertex of your network. State the minimum project completion time and list the critical activities.
Tariq does not have time to complete all the activities on his own, so he gets some help from his friend Sally.
Sally can help Tariq with any of the activities apart from \(C , H\) and \(J\). If Tariq and Sally share an activity, the time it takes is reduced by 1 hour. Sally can also do any of \(F , G\) and \(I\) on her own. - Describe how Tariq and Sally should share the work so that activity \(D\) can start 5 hours after the start of the project.
- Show that, if Sally does as much of the work as she can, she will be busy for 18 hours. In this case, for how many hours will Tariq be busy?
- Explain why, if Sally is busy for 18 hours, she will not be able to finish until more than 18 hours from the start. How soon after the start can Sally finish when she is busy for 18 hours?
- Describe how Tariq and Sally can complete the project together in 18 hours or less.