| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate lower bound for workers |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: finding early/late times, identifying the critical path, calculating a lower bound (sum of activities รท critical path length), and drawing a cascade chart. All are textbook procedures requiring no novel insight, though part (c) requires understanding the lower bound formula, making it slightly easier than average overall. |
| 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 |
9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{552f3296-ad61-448b-8168-6709fb359fa2-9_784_1531_242_267}
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\caption{Figure 7}
\end{center}
\end{figure}
Figure 7 shows an activity network. Each activity is represented by an arc and the number in brackets on each arc is the duration of the activity in days.
\begin{enumerate}[label=(\alph*)]
\item Complete Figure 7 in the answer book showing the early and late event times.
\item List the critical path for this network.
The sum of all the activity times is 95 days and each activity requires just one worker. The project must be completed in the minimum time.
\item Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must make your method clear.
\item On the grid in your answer book, draw a cascade (Gantt) chart for this network.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 Q9 [12]}}