Edexcel D1 2009 January — Question 4

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2009
SessionJanuary
TopicCombinations & Selection

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ef029462-ffed-4cdf-87bc-56c8a13d671f-4_540_626_244_316} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ef029462-ffed-4cdf-87bc-56c8a13d671f-4_531_613_246_1128} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 1 shows the possible allocations of six people, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E }\) and F , to six tasks, 1, 2, 3, 4, 5 and 6.
Figure 2 shows an initial matching.
  1. Starting from this initial matching, use the maximum matching algorithm to find an improved matching. You must list the alternating path used, and your improved matching.
  2. Explain why it is not possible to find a complete matching. D now has task 2 added to their possible allocation.
  3. Using the improved matching found in part (a) as the new initial matching, use the maximum matching algorithm to find a complete matching. You must list the alternating path used and your complete matching.
    (3)