| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question testing routine procedures: finding earliest/latest times, identifying critical path, calculating float, and drawing an activity network from a precedence table. All techniques are algorithmic and well-practiced, requiring no problem-solving insight, though part (d) requires careful attention to detail with dummies. |
| Spec | 7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation |
| Activity | Must be preceded by: | Duration |
| \(A\) | \(-\) | 4 |
| \(B\) | \(-\) | 3 |
| \(C\) | \(-\) | 5 |
| \(D\) | \(B\) | 2 |
| \(E\) | \(A, D\) | 8 |
| \(F\) | \(B\) | 2 |
| \(G\) | \(C\) | 2 |
| \(H\) | \(C\) | 3 |
| \(I\) | \(F, G\) | 4 |
| \(J\) | \(F, G\) | 2 |
| \(K\) | \(F, G\) | 7 |
| \(L\) | \(E, I\) | 9 |
| \(M\) | \(H, J\) | 3 |
| \(N\) | \(E, I, K, M\) | 3 |
| \(P\) | \(E, I\) | 6 |
| \(Q\) | \(H, J\) | 5 |
| \(R\) | \(Q\) | 7 |
\includegraphics{figure_4}
A trainee at a building company is using critical path analysis to help plan a project. Figure 4 shows the trainee's activity network. Each activity is represented by an arc and the number in brackets on each arc is the duration of the activity, in hours.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $x$, $y$ and $z$. [3]
\item State the total length of the project and list the critical activities. [2]
\item Calculate the total float time on
\begin{enumerate}[label=(\roman*)]
\item activity $N$,
\item activity $H$. [3]
\end{enumerate}
\end{enumerate}
The trainee's activity network is checked by the supervisor who finds a number of errors and omissions in the diagram. The project should be represented by the following precedence table.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Activity & Must be preceded by: & Duration \\
\hline
$A$ & $-$ & 4 \\
\hline
$B$ & $-$ & 3 \\
\hline
$C$ & $-$ & 5 \\
\hline
$D$ & $B$ & 2 \\
\hline
$E$ & $A, D$ & 8 \\
\hline
$F$ & $B$ & 2 \\
\hline
$G$ & $C$ & 2 \\
\hline
$H$ & $C$ & 3 \\
\hline
$I$ & $F, G$ & 4 \\
\hline
$J$ & $F, G$ & 2 \\
\hline
$K$ & $F, G$ & 7 \\
\hline
$L$ & $E, I$ & 9 \\
\hline
$M$ & $H, J$ & 3 \\
\hline
$N$ & $E, I, K, M$ & 3 \\
\hline
$P$ & $E, I$ & 6 \\
\hline
$Q$ & $H, J$ & 5 \\
\hline
$R$ & $Q$ & 7 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item By adding activities and dummies amend the diagram in the answer book so that it represents the precedence table. (The durations of activities $A$, $B$, ..., $N$ are all correctly given on the diagram in the answer book.) [4]
\item Find the total time needed to complete this project. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q8 [14]}}