Edexcel D1 2008 June — Question 2

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJune
TopicCombinations & Selection

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be646775-535e-4105-86b4-ffc7eda4fa51-2_432_579_1206_395} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be646775-535e-4105-86b4-ffc7eda4fa51-2_430_579_1208_1096} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Five tour guides, Alice, Emily, George, Rose and Weidi, need to be assigned to five coach trips, 1, 2, 3, 4 and 5 . A bipartite graph showing their preferences is given in Figure 1 and an initial matching is given in Figure 2.
  1. Use the maximum matching algorithm, starting with vertex G , to increase the number of matchings. State the alternating path you used.
  2. List the improved matching you found in (a).
  3. Explain why a complete matching is not possible. Weidi agrees to be assigned to coach trip 3, 4 or 5.
  4. Starting with your current maximal matching, use the maximum matching algorithm to obtain a complete matching.
    (3)