1 The diagram shows the activity network and the duration, in days, of each activity for a particular project. Some of the earliest start times and latest finish times are shown on the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{b23828c8-01ee-4b5a-b6d2-41b7e27190d6-02_830_1447_678_301}

1. Find the values of the constants \(x , y\) and \(z\).
2. Find the critical paths.
3. Find the activity with the largest float and state the value of this float.
4. The number of workers required for each activity is shown in the table.

   Activity	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)	\(J\)
   Number of workers required	4	2	3	4	2	4	3	3	5	6

   Given that each activity starts as early as possible and assuming that there is no limit to the number of workers available, draw a resource histogram for the project on Figure 1 below, indicating clearly which activities are taking place at any given time.
5. It is later discovered that there are only 9 workers available at any time. Use resource levelling to find the new earliest start time for activity \(J\) so that the project can be completed with the minimum extra time. State the minimum extra time required.
6. Number of workers \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{b23828c8-01ee-4b5a-b6d2-41b7e27190d6-03_803_1330_1224_468}
   \end{figure}