5 The network below represents a project using activity on arc. The durations of the activities are not yet shown.
\includegraphics[max width=\textwidth, alt={}, center]{490ff276-6639-40a1-bffb-dc6967f3ab21-6_597_1257_340_386}

1. If \(C\) were to turn out to be a critical activity, which two other activities would be forced to be critical?
2. Complete the table, in the Answer Book, to show the immediate predecessor(s) for each activity. In fact, \(C\) is not a critical activity. Table 1 lists the activities and their durations, in minutes. \begin{table}[h]

   Activity	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)	\(J\)
   Duration	10	15	10	5	15	5	10	15	5	15

   \captionsetup{labelformat=empty} \caption{Table 1}
   \end{table}
3. Carry out a forward pass and a backward pass through the activity network, showing the early event time and late event time at each vertex of the network. State the minimum project completion time and list the critical activities. Each activity requires one person.
4. Draw a schedule to show how three people can complete the project in the minimum time, with each activity starting at its earliest possible time. Each box in the Answer Book represents 5 minutes. For each person, write the letter of the activity they are doing in each box, or leave the box blank if the person is resting for those 5 minutes.
5. Show how two people can complete the project in the minimum time. It is required to reduce the project completion time by 10 minutes. Table 2 lists those activities for which the duration could be reduced by 5 minutes, and the cost of making each reduction. \begin{table}[h]

   Activity	\(A\)	\(B\)	\(C\)	\(E\)	\(G\)	\(H\)	\(J\)
   Cost \(( \pounds )\)	200	400	100	600	100	500	500
   New duration	5	10	5	10	5	10	10

   \captionsetup{labelformat=empty} \caption{Table 2}
   \end{table}
6. Explain why the cost of saving 5 minutes by reducing activity \(A\) is more than \(\pounds 200\). Find the cheapest way to complete the project in a time that is 10 minutes less than the original minimum project completion time. State which activities are reduced and the total cost of doing this.