| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question requiring routine application of well-defined algorithms (forward and backward pass, identifying critical path). The network is small (9 activities), the precedence relationships are straightforward, and parts (i)-(iii) follow textbook procedures. Part (iv) adds mild scheduling complexity but remains algorithmic. 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 interpretation |
| Task | Duration (seconds) | Immediate predecessors | |
| B | get out bowl and implements | 10 | - |
| I | get out ingredients | 10 | - |
| L | chop lettuce | 15 | B, I |
| W | wash tomatoes and celery | 25 | B, I |
| T | chop tomatoes | 15 | W |
| C | chop celery | 10 | W |
| P | peel apple | 20 | B, I |
| A | chop apple | 10 | P |
| D | dress salad | 10 | L, T, C, A |
6 The table shows the tasks involved in making a salad, their durations and their precedences.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{Task} & Duration (seconds) & Immediate predecessors \\
\hline
B & get out bowl and implements & 10 & - \\
\hline
I & get out ingredients & 10 & - \\
\hline
L & chop lettuce & 15 & B, I \\
\hline
W & wash tomatoes and celery & 25 & B, I \\
\hline
T & chop tomatoes & 15 & W \\
\hline
C & chop celery & 10 & W \\
\hline
P & peel apple & 20 & B, I \\
\hline
A & chop apple & 10 & P \\
\hline
D & dress salad & 10 & L, T, C, A \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity on arc network for these activities.\\
(ii) Mark on your diagram the early and late times for each event. Give the minimum completion time and the critical activities.\\
(iii) Given that each task can only be done by one person, how many people are needed to prepare the salad in the minimum time?
What is the minimum time required to prepare the salad if only one person is available?\\
(iv) Show how two people can prepare the salad as quickly as possible.
\hfill \mbox{\textit{OCR MEI D1 2012 Q6 [16]}}