8.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{a21a4565-800c-45c0-a513-bb813ef1086f-8_864_1705_356_173}
\end{figure}
A trainee at a building company is using critical path analysis to help plan a project. Figure 4 shows the trainee's activity network. Each activity is represented by an arc and the number in brackets on each arc is the duration of the activity, in hours.
- Find the values of \(x , y\) and \(z\).
- State the total length of the project and list the critical activities.
- Calculate the total float time on
- activity \(N\),
- activity \(H\).
(3)
The trainee's activity network is checked by the supervisor who finds a number of errors and omissions in the diagram. The project should be represented by the following precedence table.
| Activity | Must be preceded by: | Duration |
| A | - | 4 |
| B | - | 3 |
| C | - | 5 |
| D | B | 2 |
| E | A, \(D\) | 8 |
| \(F\) | B | 2 |
| G | C | 2 |
| \(H\) | C | 3 |
| I | \(F , G\) | 4 |
| J | \(F , G\) | 2 |
| K | \(F , G\) | 7 |
| L | E, I | 9 |
| M | H, J | 3 |
| N | E, I, K, M | 3 |
| \(P\) | E, \(I\) | 6 |
| \(Q\) | H, J | 5 |
| \(R\) | \(Q\) | 7 |
- By adding activities and dummies amend the diagram in the answer book so that it represents the precedence table. (The durations of activities \(A , B , \ldots , N\) are all correctly given on the diagram in the answer book.)
- Find the total time needed to complete this project.