| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2003 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate lower bound for workers |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: forward/backward pass, identifying critical path, calculating float, and basic scheduling. All parts follow textbook procedures with no novel problem-solving required, though part (e) requires careful application of the scheduling algorithm. Slightly easier than average due to the mechanical nature of CPA methods. |
| 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 |
\includegraphics{figure_3}
The network in Fig. 3 shows the activities involved in the process of producing a perfume. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event, showing them on Diagram 1 in the answer booklet.
[4]
\item Hence determine the critical activities.
[2]
\item Calculate the total float time for $D$.
[2]
\end{enumerate}
Each activity requires only one person.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find a lower bound for the number of workers needed to complete the process in the minimum time.
[2]
\end{enumerate}
Given that there are only three workers available, and that workers may not share an activity,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item schedule the activities so that the process is completed in the shortest time. Use the time line in the answer booklet. State the new shortest time.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2003 Q5 [15]}}