| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find range for variable duration |
| Difficulty | Standard +0.3 This is a straightforward critical path analysis question requiring basic understanding of critical paths and float calculations. Part (b) involves simple arithmetic using the critical path length, and part (c) requires calculating total float for a non-critical activity—both are standard D1 techniques with no novel problem-solving required. Slightly easier than average due to being given which activities are critical. |
| 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 interpretation |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | - |
| D | A |
| E | A |
| F | A, B, C |
| G | C |
| H | E, F, G |
| I | E, F, G |
| J | H, I |
| K | H, I |
| L | D, J |
| Activity | Duration (in days) |
| B | 7 |
| F | 4 |
| J | 4 |
| L | 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| [Diagram showing network with activities and arrows] | M1, A1, A1, A1, A1 | (5) |
| \(I = 9\) | B1 | (1) |
| \(7 + 4 + (\text{their I}) + K < 30\) or \(K < J + L\); \(0 < K < 10\) (accept \(0 \leq K < 10\)) or \(1 \leq K \leq 9\) | M1, A1 | (2) |
| 8 marks |
| Answer/Working | Marks | Guidance |
|---|---|---|
| [Diagram showing network with activities and arrows] | M1, A1, A1, A1, A1 | (5) |
| $I = 9$ | B1 | (1) |
| $7 + 4 + (\text{their I}) + K < 30$ or $K < J + L$; $0 < K < 10$ (accept $0 \leq K < 10$) or $1 \leq K \leq 9$ | M1, A1 | (2) |
| | | **8 marks** |
**Notes for Question 4:**
- Condone lack of, or incorrect, numbered events throughout and arcs which cross one another. 'Dealt with correctly' means that the activity starts from the correct event but need not necessarily finish at the correct event, e.g. 'H dealt with correctly' requires the correct precedences for this activity, i.e. E, F and G labelled correctly and leading into the same node and H starting from that node but not H need not end in the correct place. **Activity on node is M0**
- **Ignore incorrect or lack of arrows on the activities for the first four marks only**
- a1M1: 7 activities (labelled on arc), one start and one dummy placed
- a1A1: Activities A, B, C, D, E and G dealt with correctly
- a2A1: Activities F, H, I and the two dummies (+ arrows) at the end of activities A and C leading into the end of activity B dealt with correctly
- a3A1: Activities J, K, L and the dummy (+ arrow) at the end of activities H and I dealt with correctly
- a4A1: CSO – all arrows present and correctly placed with one finish (with no extra dummies)
- b1B1: CAO
- c1M1: $K < 30 - 7 - 4 - (\text{their I})$ or $K < 10$ or $K \leq 9$ or $K \leq 30 - 7 - 4 - (\text{their I}) - 1$
- c1A1: CAO (see main scheme for the three acceptable answers)
---4. (a) Draw the activity network described in the precedence table below, using activity on arc and the minimum number of dummies.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & A \\
\hline
E & A \\
\hline
F & A, B, C \\
\hline
G & C \\
\hline
H & E, F, G \\
\hline
I & E, F, G \\
\hline
J & H, I \\
\hline
K & H, I \\
\hline
L & D, J \\
\hline
\end{tabular}
\end{center}
A project is modelled by the activity network drawn in (a). Each activity requires one worker. The project is to be completed in the shortest possible time. The table below gives the time, in days, to complete some of the activities.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Activity & Duration (in days) \\
\hline
B & 7 \\
\hline
F & 4 \\
\hline
J & 4 \\
\hline
L & 6 \\
\hline
\end{tabular}
\end{center}
The critical activities for the project are B, F, I, J and L and the length of the critical path is 30 days.\\
(b) Calculate the duration of activity I.\\
(c) Find the range of possible values for the duration of activity K .\\
\hfill \mbox{\textit{Edexcel D1 2016 Q4 [8]}}