| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2017 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate lower bound for workers |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question covering routine D1 techniques: finding early/late times, identifying critical paths, and calculating lower bounds using total activity time divided by project duration. Part (e) specifically requires only a straightforward formula application (sum of durations / critical path length), making it easier than average A-level questions which typically require more problem-solving. |
| 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]
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\includegraphics[alt={},max width=\textwidth]{8c9bce2c-4156-4bf6-8d02-9e01d6f11948-08_1024_1495_226_276}
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\caption{Figure 5}
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A project is modelled by the activity network shown in Figure 5. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the corresponding activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Complete Diagram 1 in the answer book to show the early event times and late event times.
\item Explain what is meant by a critical path.
\item List the critical path for this network.
\item For each of the situations below, state the effect that the delay would have on the project completion date.
\begin{enumerate}[label=(\roman*)]
\item A 4-day delay during activity J.
\item A 4-day delay during activity M .
The delays mentioned in (d) do not occur.
\end{enumerate}\item Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
\item Schedule the activities using the minimum number of workers so that the project is completed in the minimum time.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2017 Q7 [14]}}