Moderate -0.3 This is a standard D1 critical path analysis question requiring students to find a range for a variable duration. While it involves multiple steps (understanding the critical path, using the given total, and setting up inequalities), the method is routine and well-practiced. The question provides significant scaffolding (the critical path is given, key durations are provided) and requires only straightforward algebraic manipulation once the concept is understood. Slightly easier than average due to the structured nature and standard technique.
Draw the activity network described in the precedence table above, using activity on arc and the minimum number of dummies.
A project is modelled by the activity network drawn in (a). Each activity requires exactly one worker. The project is to be completed in the shortest possible time. The table below gives the time, in hours, to complete three of the activities.
Activity
Duration (in hours)
A
10
E
7
F
8
The length of the critical path AEFK is 33 hours.
Determine the range of possible values for the duration of activity J. You must make your method and working clear.
5.
\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 & B, C, E \\
\hline
G & B, C, E \\
\hline
H & C \\
\hline
I & C \\
\hline
J & D, F, G, H, I \\
\hline
K & D, F, G, H, I \\
\hline
L & I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table above, using activity on arc and the minimum number of dummies.
A project is modelled by the activity network drawn in (a). Each activity requires exactly one worker. The project is to be completed in the shortest possible time. The table below gives the time, in hours, to complete three of the activities.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Activity & Duration (in hours) \\
\hline
A & 10 \\
\hline
E & 7 \\
\hline
F & 8 \\
\hline
\end{tabular}
\end{center}
The length of the critical path AEFK is 33 hours.
\item Determine the range of possible values for the duration of activity J. You must make your method and working clear.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2023 Q5 [7]}}