AQA D1 2008 January — Question 1

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJanuary
TopicMatchings and Allocation

1 Five people, \(A , B , C , D\) and \(E\), are to be matched to five tasks, \(J , K , L , M\) and \(N\). The table shows the tasks that each person is able to undertake.
PersonTask
\(A\)\(J , N\)
\(B\)\(J , L\)
\(C\)\(L , N\)
\(D\)\(M , N\)
\(E\)\(K , M\)
  1. Show this information on a bipartite graph.
  2. Initially, \(A\) is matched to task \(N , B\) to task \(J , C\) to task \(L\), and \(E\) to task \(M\). Complete the alternating path \(D - M \ldots\), from this initial matching, to demonstrate how each person can be matched to a task.
    (3 marks)