2. A company manages an awards evening.

The table below lists the activities required to set up the room for the evening, and their immediately preceding activities. Each activity requires exactly one person.

\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & A \\
\hline
C & A \\
\hline
D & C \\
\hline
E & C \\
\hline
F & B, D, E \\
\hline
G & E \\
\hline
H & B \\
\hline
J & H, F, G \\
\hline
\end{tabular}
\end{center}

Figure 1 shows a partially completed activity network used to model the project. Each activity is represented by an arc.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-04_440_813_1689_726}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item Add the remaining five activities to Diagram 1 in the answer book to complete the activity network, using exactly two dummies.

In addition to setting up the room, the company must prepare the meals for the guests. Figure 2 shows the activity network for preparing the main courses. The numbers in brackets represent the time, in minutes, to complete each task.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-05_793_1515_451_373}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
\item Complete Diagram 2 in the answer book to show the early event times and the late event times for the activity network shown in Figure 2.
\item State the critical activities.
\item Given that the main courses need to be ready to be served (with all activities completed) at 8 pm , state the latest time that activity $R$ can start.
\end{enumerate}

\hfill \mbox{\textit{Edexcel FD1 AS 2024 Q2 [8]}}