Edexcel D1 2013 June — Question 1

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2013
SessionJune
TopicCombinations & Selection

1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1493d74b-e9ef-4c9a-91f6-877c1eaa74e2-02_533_551_365_402} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1493d74b-e9ef-4c9a-91f6-877c1eaa74e2-02_529_545_365_1098} \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 the given initial matching, use the maximum matching algorithm to find an improved matching. You should list the alternating path you used, and your improved matching.
  2. Explain why it is not possible to find a complete matching. After training, task 4 is added to F's possible allocation and task 6 is added to E's possible allocation.
  3. Starting from the improved matching found in (a), use the maximum matching algorithm to find a complete matching. You should list the alternating path you used and your complete matching.