Edexcel D1 2009 June — Question 3

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2009
SessionJune
TopicMatchings and Allocation

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c1482d20-7bce-46cb-9ac8-c659ecad30de-3_755_624_283_283} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c1482d20-7bce-46cb-9ac8-c659ecad30de-3_750_620_285_1146} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 1 shows the possible allocations of six workers, Charlotte (C), Eleanor (E), Harry (H), Matt (M), Rachel (R) and Simon (S) to six tasks, 1, 2, 3, 4, 5 and 6. Figure 2 shows an initial matching.
  1. List an alternating path, starting at H and ending at 4 . Use your path to find an improved matching. List your improved matching.
  2. Explain why it is not possible to find a complete matching. Simon (S) now has task 3 added to his possible allocation.
  3. Taking the improved matching found in (a) as the new initial matching, use the maximum matching algorithm to find a complete matching. List clearly the alternating path you use and your complete matching.
    (3)