| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Complete precedence table from network |
| Difficulty | Standard +0.3 This is a standard D1 critical path analysis question covering routine procedures: reading a network diagram to complete a precedence table, explaining dummies, finding early/late times, identifying critical path, calculating float, and finding a lower bound for workers. All parts follow textbook algorithms with no novel problem-solving required, making it slightly easier than average. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0360f78d-e18c-4c47-a2ec-ddd705a4175f-8_888_1701_198_180}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{center}
\end{figure}
The network in Figure 7 shows the activities that need to be undertaken to complete a maintenance project. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. The numbers in circles are the events.
Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Complete the precedence table for this network in the answer book.
\item Explain why each of the following is necessary.
\begin{enumerate}[label=(\roman*)]
\item The dummy from event 6 to event 7 .
\item The dummy from event 8 to event 9 .
\end{enumerate}\item Complete Diagram 2 in the answer book to show the early and the late event times.
\item State the critical activities.
\item Calculate the total float on activity K . You must make the numbers used in your calculation clear.
\item Calculate a lower bound for the number of workers needed to complete the project in the minimum time.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2011 Q7 [16]}}