| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate lower bound for workers |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question from D1 covering routine techniques: finding early/late times, calculating float, identifying critical path, and applying the lower bound formula (sum of activity times divided by project duration). Part (d) requires only a simple calculation using a well-known formula, making this easier than average despite being multi-part. |
| 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 interpretation7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Top 3 boxes completed, generally ascending L to R (values 17, 18, 20 shown) | M1, A1 | cao |
| Bottom 4 boxes completed, generally descending R to L (values 35, 20, 8, 14 shown) | M1, A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total float on \(D = 18 - 5 - 9 = 4\) | M1, A1ft | Correct (ft) three numbers visible for at least one calculation; one correct value (ft on D) |
| \(G = 25 - 8 - 10 = 7\) | A1 | 2 correct values |
| \(I = 25 - 20 - 3 = 2\) | B1 | 3 correct values (even if no working seen) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities: \(B, E, J, M\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Lower bound \(= \dfrac{102}{35} = 2.914\) | M1 | \(102 \div 35\)ft |
| \(\therefore 3\) workers | A1 | cao |
# Question 4:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Top 3 boxes completed, generally ascending L to R (values 17, 18, 20 shown) | M1, A1 | cao |
| Bottom 4 boxes completed, generally descending R to L (values 35, 20, 8, 14 shown) | M1, A1 | cao |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total float on $D = 18 - 5 - 9 = 4$ | M1, A1ft | Correct (ft) three numbers visible for at least one calculation; one correct value (ft on D) |
| $G = 25 - 8 - 10 = 7$ | A1 | 2 correct values |
| $I = 25 - 20 - 3 = 2$ | B1 | 3 correct values (even if no working seen) |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: $B, E, J, M$ | B1 | cao |
## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower bound $= \dfrac{102}{35} = 2.914$ | M1 | $102 \div 35$ft |
| $\therefore 3$ workers | A1 | cao |
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{7396d930-0143-4876-b019-a4d73e09b172-5_1079_1392_267_338}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
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. Some of the early and late times for each event are shown.
\begin{enumerate}[label=(\alph*)]
\item Calculate the missing early and late times and hence complete Diagram 1 in your answer book.
\item Calculate the total float on activities D, G and I. You must make your calculations clear.
\item List the critical activities.
Each activity requires one worker.
\item Calculate a lower bound for the number of workers needed to complete the project in the minimum time.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2008 Q4 [11]}}