3.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bd6edbd4-1ec0-4c7e-bd39-b88f96bf52fb-3_743_625_758_269}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bd6edbd4-1ec0-4c7e-bd39-b88f96bf52fb-3_746_608_758_1142}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 2 shows the possible allocations of six workers, Charlie (C), George (G), Jack (J), Nurry (N), Olivia (O) and Rachel (R), to six tasks, $1,2,3,4,5$ and 6.

Figure 3 shows an initial matching.
\begin{enumerate}[label=(\alph*)]
\item Starting from this initial matching, use the maximum matching algorithm to find an improved matching. You should give the alternating path you use and list your improved matching.
\item Explain why it is not possible to find a complete matching.

After training, Charlie adds task 5 to his possible allocations.
\item Taking the improved matching found in (a) as the new initial matching, use the maximum matching algorithm to find a complete matching. Give the alternating path you use and list your complete matching.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2013 Q3 [8]}}