6. The precedence table below shows the twelve activities required to complete a project.
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | - |
| D | A |
| E | A, B |
| F | D, E |
| G | A, B, C |
| H | F, G |
| I | D, E |
| J | D, E |
| K | F, G, I, J |
| L | I |
- Draw the activity network described in the precedence table, using activity on arc. Your activity network must contain the minimum number of dummies only.
(5)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6ccce35f-4e62-4b6b-acf6-f9b3e18d4b52-11_654_1358_153_356}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
Figure 6 shows a partially completed cascade chart for the project. The non-critical activities F, J and K are not shown in Figure 6.
The time taken to complete each activity is given in hours and the project is to be completed in the minimum possible time. - State the critical activities.
Given that the total float of activity F is 2 hours,
- state the duration of activity F .
The duration of activity J is \(x\) hours, and the duration of activity K is \(y\) hours, where \(x > 0\) and \(y > 0\)
- State, in terms of \(y\), the maximum possible total float for activity K.
- State, in terms of \(x\) and \(y\), the total float for activity J .