| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - create schedule/chart |
| Difficulty | Standard +0.3 This is a standard D1 critical path analysis question with resource allocation. Parts (a)-(c) are routine textbook exercises (finding early/late times, critical path, minimum time). Parts (d)-(e) add worker constraints requiring a simple schedule chart, which is a common D1 exam technique but straightforward once the critical path is known. Slightly easier than average due to being a well-practiced topic with mechanical procedures. |
| 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 |
| \(P\) | \(\bullet\) | \(\bullet\) | \(D\) |
| \(Q\) | \(\bullet\) | \(\bullet\) | \(G\) |
| \(R\) | \(\bullet\) | \(\bullet\) | \(E\) |
| \(S\) | \(\bullet\) | \(\bullet\) | \(L ( H )\) |
| \(T\) | \(\bullet\) | \(\bullet\) | \(L\) |
| \(x\) | \(a\) | \(b\) | \(( a - b ) < 0.01\) ? |
| 100 | 50 | 26 | No |
| - | 26 | 14.923 | No |
| \(x\) | \(a\) | \(b\) | \(( a - b ) < 0.01 ?\) |
| 100 |
| 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| Worker 1 | ||||||||||||
| Worker 2 |
| 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| Worker 1 | ||||||||||||
| Worker 2 | ||||||||||||
| Worker 3 |
| Answer | Marks |
|---|---|
| ] | M3 A3 |
| Answer | Marks |
|---|---|
| C, I, K, L, M, O | M1 A1 |
| Answer | Marks |
|---|---|
| 56 days | A1 |
| Answer | Marks |
|---|---|
| ] | B2 |
| Answer | Marks | Guidance |
|---|---|---|
| ] | M1 A2 | (14) |
**Part (a)**
[Critical path network diagram showing:
- Start node (0)
- Activity nodes with durations: A(12), B(5), C(10), D(0), E(0), F(8), G(5), H(8), I(17), J(11), K(6), L(6), M(9), N(2), O(8), P(5)
- Nodes labeled with earliest and latest times
- End node showing 56
] | M3 A3 |
**Part (b)**
C, I, K, L, M, O | M1 A1 |
**Part (c)**
56 days | A1 |
**Part (d)**
[Gantt chart showing:
Worker 1: C (0-10), I (10-27), K (27-33), L (33-39), M (39-48), O (48-56)
Worker 2: A (0-12), B (12-17)
Note: with worker 1 doing tasks on critical path, worker 2 can do A and B but no worker is available to start F after 14 minutes so not possible
] | B2 |
**Part (e)**
[Gantt chart showing:
Worker 1: C (0-10), I (10-27), K (27-33), L (33-39), M (39-48), O (48-56)
Worker 2: A (0-12), F (12-20), J (20-31), N (51-53), P (53-58)
Worker 3: B (0-5), G (5-13), H (13-21)
] | M1 A2 | (14) |
---
**Total: (75)**7. This question should be answered on the sheet provided.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1e518ab0-9852-4d1d-a4c9-344a5edf9547-07_576_1360_331_278}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Figure 2 shows an activity network modelling the tasks involved in widening a bridge over the B451. The arcs represent the tasks and the numbers in brackets gives the time, in days, to complete each task.
\begin{enumerate}[label=(\alph*)]
\item Find the early and late times for each event.
\item Determine those activities which lie on the critical path and list them in order.
\item State the minimum length of time needed to widen the bridge.
Each task needs a single worker.
\item Show that two men would not be sufficient to widen the bridge in the shortest time.\\
(2 marks)
\item Draw up a schedule showing how 3 men could complete the project in the shortest time.
\section*{Please hand this sheet in for marking}
(a)
Complete matching:
\begin{center}
\begin{tabular}{ l l l l }
$P$ & $\bullet$ & $\bullet$ & $D$ \\
$Q$ & $\bullet$ & $\bullet$ & $G$ \\
$R$ & $\bullet$ & $\bullet$ & $E$ \\
$S$ & $\bullet$ & $\bullet$ & $L ( H )$ \\
$T$ & $\bullet$ & $\bullet$ & $L$ \\
\end{tabular}
\end{center}
\section*{Please hand this sheet in for marking}
(a)
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
$x$ & $a$ & $b$ & $( a - b ) < 0.01$ ? \\
\hline
100 & 50 & 26 & No \\
\hline
- & 26 & 14.923 & No \\
\hline
\end{tabular}
\end{center}
Final output\\
(b) $\_\_\_\_$\\
(c)
\begin{center}
\begin{tabular}{ c | l | l | l | }
$x$ & $a$ & $b$ & $( a - b ) < 0.01 ?$ \\
100 & & & \\
\end{tabular}
\end{center}
(d) $\_\_\_\_$\\
\section*{Please hand this sheet in for marking}
(a)\\
\includegraphics[max width=\textwidth, alt={}, center]{1e518ab0-9852-4d1d-a4c9-344a5edf9547-11_768_1689_427_221}\\
(b) $\_\_\_\_$\\
(c) $\_\_\_\_$\\
(d)
\begin{center}
\begin{tabular}{ l | l | l | l | l | l | l | l | l | l | l | l | l }
\multicolumn{1}{c}{0} & \multicolumn{1}{c}{5} & \multicolumn{1}{c}{10} & \multicolumn{1}{c}{15} & \multicolumn{1}{c}{20} & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 \\
\hline
Worker 1 & & & & & & & & & & & & \\
\hline
Worker 2 & & & & & & & & & & & & \\
\hline
\end{tabular}
\end{center}
(e)
\begin{center}
\begin{tabular}{ c | l | l | l | l | l | l | l | l | l | l | l | l | }
\multicolumn{1}{c}{0} & \multicolumn{1}{c}{5} & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 \\
\hline
Worker 1 & & & & & & & & & & & & \\
\hline
Worker 2 & & & & & & & & & & & & \\
\hline
Worker 3 & & & & & & & & & & & & \\
\hline
\end{tabular}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 Q7 [14]}}