7.
| Activity | Time taken (days) | Immediately preceding activities |
| A | 5 | - |
| B | 7 | - |
| C | 8 | - |
| D | 5 | A |
| E | 7 | A |
| F | 10 | B, C |
| G | 4 | B, C |
| H | 9 | C |
| I | 8 | G, H |
| J | 12 | G, H |
| K | 7 | D |
| L | 10 | E, F, I, J |
The table shows the activities required for the completion of a building project. For each activity the table shows the time taken, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba22b22e-c0d5-438d-821b-88619eacdb5d-8_768_1162_1238_431}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
Figure 6 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the numbers in brackets on the arcs are the times taken, in days, to complete each activity.
- Add activities, E, F and I, and exactly one dummy to Diagram 1 in the answer book.
- Complete Diagram 1 in the answer book to show the early event times and late event times.
- Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.
(2) - Schedule the activities, using the minimum number of workers, so that the project is completed in the minimum time.
(Total 13 marks)