Identify guaranteed critical activities

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.

5.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies.
   (5) Given that D is a critical activity,
2. state which other activities must also be critical.
   (1)

5.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies. Given that all critical paths for the network include activity H ,
2. state which activities cannot be critical.
   (2)

4.

1. Draw the activity network described in the precedence table, using activity on arc and the minimum number of dummies.
2. Given that
   • the activity network contains only one critical path
   • activity E is on this critical path
     state
     1. which activities could never be critical,
     2. which activities must be critical.

4. (a) Draw the activity network described by the precedence table below, using activity on arc. Use dummies only where necessary.
(5) Given that K is a critical activity,
(b) state which other activities must also be critical.
(1) Given instead that all activities shown in the precedence table have the same duration and K is not necessarily critical,
(c) state the critical path for the network.
(1)

6.

1. Draw the activity network for the project described in the precedence table above, using activity on arc and the minimum number of dummies.
   (5)
2. State which activity is guaranteed to be critical, giving a reason for your answer.
   (2) It is given that each activity in the table takes two hours to complete.
3. State the minimum completion time and write down the critical path for the project.
   (2)

3. (a) Draw the activity network described in the precedence table below, using activity on arc and exactly four dummies.
(5) Given that D is a critical activity,
(b) state which other activities must also be critical.
(2)

5.

1. Draw the activity network described in the precedence table above, using activity on arc and exactly 4 dummies.
2. Explain why one of the activities I or J must be critical. It is given that activity C is a critical activity.
3. State the activities that are therefore guaranteed to be critical.

2.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies only.
2. Explain why it is necessary to draw a dummy from the end of activity A . Every activity shown in the precedence table has the same duration.
3. State which activity cannot be critical, justifying your answer.

5.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies. Given that all the activities shown in the precedence table have the same duration, (b) state the critical path for the network.

7. \begin{figure}[h] \end{figure} Figure 5 shows a partially completed activity network for a project that consists of 14 activities.

1. Complete the precedence table in the answer book for the 8 activities in Figure 5. The precedence table for the remaining 6 activities is given below.

   Activity	Immediately preceding activities
   I	D, E, G, H
   J	D, E, G, H
   K	E, G, H
   L	I, J, K
   M	J, K
   N	J, K

2. Complete the activity network in the answer book for the project. Your completed activity network must contain only the minimum number of dummies. Given that all 14 activities have the same duration,
3. explain why activity D cannot be critical.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies. [5]

Every activity shown in the precedence table has the same duration.

1. Explain why activity B cannot be critical. [1]
2. State which other activities are not critical. [1]