| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - create schedule/chart |
| Difficulty | Moderate -0.3 This is a standard D1 critical path question with routine parts: drawing a network (mechanical application of rules), reading critical activities from a given cascade chart, counting workers from the chart (visual inspection), and calculating float (simple arithmetic). All parts follow textbook procedures 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 |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | A |
| D | - |
| E | A, B, D |
| F | D |
| G | A, B, D |
| H | F, G |
| I | A |
| J | F, G |
| K | C, E, H, I |
| L | I |
| M | C, E, H, I |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| 6(a) | Network diagram with appropriate nodes and arcs showing the precedence relationships correctly | M1, A1 (ABDICF), A1 (EGHHJ), A1 (KLOM), A1 (5) |
| 6(b) | Activities B, G, H and M are critical | B1 (1) |
| 6(c) | At time 9.5, activities G, C, E and I must all be happening therefore a minimum of 4 workers is required | M1 A1 (2) |
| 6(d) | \(2 \leq x \leq 6\) | B2, 1, 0 (2) |
| Total: 10 marks |
| Part | Answer/Working | Marks | Guidance |
|------|---|---|---|
| 6(a) | Network diagram with appropriate nodes and arcs showing the precedence relationships correctly | M1, A1 (ABDICF), A1 (EGHHJ), A1 (KLOM), A1 (5) | |
| 6(b) | Activities B, G, H and M are critical | B1 (1) | |
| 6(c) | At time 9.5, activities G, C, E and I must all be happening therefore a minimum of 4 workers is required | M1 A1 (2) | |
| 6(d) | $2 \leq x \leq 6$ | B2, 1, 0 (2) | |
| | **Total: 10 marks** | | |
---6.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & A \\
\hline
D & - \\
\hline
E & A, B, D \\
\hline
F & D \\
\hline
G & A, B, D \\
\hline
H & F, G \\
\hline
I & A \\
\hline
J & F, G \\
\hline
K & C, E, H, I \\
\hline
L & I \\
\hline
M & C, E, H, I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network for the project described in the precedence table, using activity on arc and the minimum number of dummies.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-10_880_1154_1464_452}
\captionsetup{labelformat=empty}
\caption{Grid 1}
\end{center}
\end{figure}
A cascade chart for all the activities of the project, except activity $\mathbf { L }$, is shown on Grid 1.
The time taken to complete each activity is given in hours and each activity requires one worker.
The project is to be completed in the minimum time using as few workers as possible.
\item State the critical activities of the project.
\item Use the cascade chart 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. (You do not need to provide a schedule of the activities.)
The duration of activity L is $x$ hours. Given that the total float of activity L is at most 7 hours,
\item determine the range of possible values for $\chi$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2024 Q6 [10]}}