8.
\begin{figure}[h]
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\caption{Figure 5}
\includegraphics[alt={},max width=\textwidth]{4bbe6272-3900-42de-b287-599638ca75e4-10_1042_1847_335_115}
\end{figure}
The network in Figure 5 shows activities that need to be undertaken in order to complete a project. Each activity is represented by an arc. The number in brackets is the duration of the activity in hours. The early and late event times are shown at each node. The project can be completed in 24 hours.
- Find the values of \(x , y\) and \(z\).
- Explain the use of the dummy activity in Figure 5.
- List the critical activities.
- Explain what effect a delay of one hour to activity \(B\) would have on the time taken to complete the whole project.
The company which is to undertake this project has only two full time workers available. The project must be completed in 24 hours and in order to achieve this, the company is prepared to hire additional workers at a cost of \(\pounds 28\) per hour. The company wishes to minimise the money spent on additional workers. Any worker can undertake any task and each task requires only one worker.
- Explain why the company will have to hire additional workers in order to complete the project in 24 hours.
- Schedule the tasks to workers so that the project is completed in 24 hours and at minimum cost to the company.
- State the minimum extra cost to the company.