| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Interpret optimal tableau |
| Difficulty | Moderate -0.8 This is a standard critical path analysis question covering routine D1 techniques: finding early/late times, identifying critical activities, calculating float, and drawing a Gantt chart. While multi-part with 15 marks total, each component is a textbook exercise requiring methodical application of well-defined algorithms rather than problem-solving or insight. The final part requires simple reading from the Gantt chart. Easier than average A-level maths. |
| 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 |
|---|---|
| (a) [Network diagram] | m1 A1(2) |
| (b) \(A - C - G - I - M > H - K\) | A1(1) |
| (c) Float on D: 21 - 5 - 14 = 2; Float on F: 42 - 10 - 14 = 8 | B1 m A1(3) |
| (d) [Gantt chart showing activities A through O with dependencies] | m1 A1(4) |
| (e) Day 15: C; Day 25: G, H, E, F | B1 B2,1(3) |
(a) [Network diagram] | m1 A1(2)
(b) $A - C - G - I - M > H - K$ | A1(1)
(c) Float on D: 21 - 5 - 14 = 2; Float on F: 42 - 10 - 14 = 8 | B1 m A1(3)
(d) [Gantt chart showing activities A through O with dependencies] | m1 A1(4)
(e) Day 15: C; Day 25: G, H, E, F | B1 B2,1(3)
---\includegraphics{figure_4}
An engineering project is modelled by the activity network shown in Figure 4. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest time.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and late time for each event. Write these in boxes in Diagram 1 in the answer book. [4]
\item State the critical activities. [1]
\item Find the total float on activities D and F. You must show your working. [3]
\item On the grid in the answer book, draw a cascade (Gantt) chart for this project. [4]
\end{enumerate}
The chief engineer visits the project on day 15 and day 25 to check the progress of the work. Given that the project is on schedule,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item which activities must be happening on each of these two days? [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2006 Q5 [15]}}