| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2007 |
| Session | January |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Explain dummy activities |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question covering routine D1 techniques: identifying dummy activities, calculating early/late times, finding float and critical path, and basic scheduling. All parts follow textbook procedures with no novel problem-solving required, making it easier than average A-level maths questions. |
| 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 |
| Answer | Marks |
|---|---|
| J depends on H alone, but L depends on H and I | B1 (1) |
| Answer | Marks |
|---|---|
| [Network diagram showing activities with durations and dependencies] | M1, A1, M1, A1 (4) |
| Answer | Marks |
|---|---|
| Total float on D = \(20 - 7 - 3 = 5\) / Total float on E = \(20 - 11 - 9 = 0\) / Total float on F = \(29 - 5 - 8 = 16\) | M1, A1 (2) |
| Answer | Marks |
|---|---|
| \(C - E \to H - J \to M\) with \(K\) and other paths shown | M1, A1 (2) |
| Answer | Marks |
|---|---|
| \(\frac{45}{38} = 2.5\) so 3 workers | M1, A1 (2) |
| Answer | Marks |
|---|---|
| [Resource histogram showing allocation across time period 0-40] | M1, A1, A1, A1 (4), [16] |
## 6(a)
| J depends on H alone, but L depends on H and I | B1 (1) |
## 6(b)
| [Network diagram showing activities with durations and dependencies] | M1, A1, M1, A1 (4) |
## 6(c)
| Total float on D = $20 - 7 - 3 = 5$ / Total float on E = $20 - 11 - 9 = 0$ / Total float on F = $29 - 5 - 8 = 16$ | M1, A1 (2) |
## 6(d)
| $C - E \to H - J \to M$ with $K$ and other paths shown | M1, A1 (2) |
## 6(e)
| $\frac{45}{38} = 2.5$ so 3 workers | M1, A1 (2) |
## 6(f)
| [Resource histogram showing allocation across time period 0-40] | M1, A1, A1, A1 (4), [16] |\includegraphics{figure_5}
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 hours, to complete the activity. The numbers in circles are the event numbers. Each activity requires one worker.
\begin{enumerate}[label=(\alph*)]
\item Explain the purpose of the dotted line from event 6 to event 8. (1)
\item Calculate the early time and late time for each event. Write these in the boxes in the answer book. (4)
\item Calculate the total float on activities $D$, $E$ and $F$. (3)
\item Determine the critical activities. (2)
\item Given that the sum of all the times of the activities is 95 hours, calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working. (2)
\item Given that workers may not share an activity, schedule the activities so that the process is completed in the shortest time using the minimum number of workers. (4)
\end{enumerate}
(Total 16 marks)
\hfill \mbox{\textit{Edexcel D1 2007 Q6}}