| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find missing early/late times |
| Difficulty | Standard +0.3 This is a standard Critical Path Analysis question requiring systematic application of forward/backward pass algorithms and float calculations. While it involves multiple steps and algebraic manipulation (finding x and y using given constraints), the techniques are routine D1 procedures with no novel problem-solving required. The cascade chart in part (c) is a straightforward application once the network is solved. Slightly easier than average due to being a textbook-style CPA question. |
| 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 float7.05e Cascade charts: scheduling and effect of delays |
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{27296f39-bd03-47ff-9a5e-c2212d0c68ed-03_977_1537_205_264}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration of the activity, in days, is shown in brackets. The early event times and late event times are to be shown at each vertex and some have been completed.
Given that
\begin{itemize}
\item CHN is the critical path for the project
\item the total float on activity B is twice the duration of the total float on activity I
\begin{enumerate}[label=(\alph*)]
\item find the value of $x$ and show that the value of $y$ is 7
\item Calculate the missing early event times and late event times and hence complete Diagram 1 in your answer book.
\end{itemize}
Each activity requires one worker, and the project must be completed in the shortest possible time.
\item Draw a cascade chart for this project on Grid 1 in your answer book, and use it to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2022 Q2 [11]}}