| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question covering routine techniques: finding early/late times, identifying critical activities, calculating float, and drawing a Gantt chart. While multi-part with 6 sections, each part applies textbook algorithms without requiring novel insight or complex problem-solving. The cascade chart drawing is time-consuming but procedural. Slightly easier than average due to the algorithmic nature of CPA. |
| Spec | 7.05b 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 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(v = 16, w = 25, x = 23, y = 20, z = 8\) | B3, 2, 1, 0 | (3 marks) |
| (b) B C G L M Q | B1 | (1 mark) |
| (c) Float on H = 23ft – 19 – 3 = 1; Float on J = 25 – 22 – 2 = 1 | B1 B1 | (2 marks) |
| (d) [Gantt chart with activities A through Q correctly positioned] | M1 A1 A1 A1 | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| (e) E has one day of float, so project can still be completed on time. | B2, 1, 0 | (2 marks) |
| (f) e.g. At time 23 ½ activities L, I and J must be taking place. At time 13 ½ or 14 ½ activities C, D, E and F must be taking place. So 4 workers needed. | B2, 1, 0 | (2 marks) |
**(a)** $v = 16, w = 25, x = 23, y = 20, z = 8$ | B3, 2, 1, 0 | (3 marks) |
**(b)** B C G L M Q | B1 | (1 mark) |
**(c)** Float on H = 23ft – 19 – 3 = 1; Float on J = 25 – 22 – 2 = 1 | B1 B1 | (2 marks) |
**(d)** [Gantt chart with activities A through Q correctly positioned] | M1 A1 A1 A1 | (4 marks) |
**Guidance:** M1: CAO. A1: CAO. A1: CAO. A1: CAO.
**(e)** E has one day of float, so project can still be completed on time. | B2, 1, 0 | (2 marks) |
**(f)** e.g. At time 23 ½ activities L, I and J must be taking place. At time 13 ½ or 14 ½ activities C, D, E and F must be taking place. So 4 workers needed. | B2, 1, 0 | (2 marks) |
**Total for Q7: 14 marks**
---7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{be646775-535e-4105-86b4-ffc7eda4fa51-7_769_1385_262_342}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
The network in Figure 6 shows the activities that need to be undertaken to complete a building project. Each activity is represented by an arc. The number in brackets is the duration of the activity in days. The early and late event times are shown at each vertex.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $v , w , x , y$ and $z$.
\item List the critical activities.
\item Calculate the total float on each of activities H and J .
\item Draw a cascade (Gantt) chart for the project.
The engineer in charge of the project visits the site at midday on day 8 and sees that activity E has not yet been started.
\item Determine if the project can still be completed on time. You must explain your answer.
Given that each activity requires one worker and that the project must be completed in 35 days,
\item use your cascade chart to determine a lower bound for the number of workers needed. You must justify your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2008 Q7 [14]}}