2. \begin{figure}[h] \end{figure} The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in hours, of the corresponding activity is shown in brackets.

1. Explain why each of the dummy activities is required.
2. Complete the table in the answer book to show the immediately preceding activities for each activity.
3. 1. Complete Diagram 1 in the answer book to show the early event times and the late event times.
   2. State the minimum completion time for the project.
   3. State the critical activities. Each activity requires one worker. Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption.
4. On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time.
5. Determine whether or not the project can be completed in the minimum possible time using fewer workers than the number indicated by the resource histogram in (d). You must justify your answer with reference to the resource histogram and the completed Diagram 1.