6. The precedence table below shows the twelve activities required to complete a project.

\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & A \\
\hline
E & A, B \\
\hline
F & D, E \\
\hline
G & A, B, C \\
\hline
H & F, G \\
\hline
I & D, E \\
\hline
J & D, E \\
\hline
K & F, G, I, J \\
\hline
L & I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table, using activity on arc. Your activity network must contain the minimum number of dummies only.\\
(5)

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{6ccce35f-4e62-4b6b-acf6-f9b3e18d4b52-11_654_1358_153_356}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}

Figure 6 shows a partially completed cascade chart for the project. The non-critical activities F, J and K are not shown in Figure 6.

The time taken to complete each activity is given in hours and the project is to be completed in the minimum possible time.
\item State the critical activities.

Given that the total float of activity F is 2 hours,
\item state the duration of activity F .

The duration of activity J is $x$ hours, and the duration of activity K is $y$ hours, where $x > 0$ and $y > 0$
\item \begin{enumerate}[label=(\roman*)]
\item State, in terms of $y$, the maximum possible total float for activity K.
\item State, in terms of $x$ and $y$, the total float for activity J .
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{Edexcel FD1 2023 Q6 [9]}}