AQA D1 2013 June — Question 1

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2013
SessionJune
TopicPermutations & Arrangements
TypeAssignment/allocation matching problems

1 Six people, Andy, Bob, Colin, Dev, Eric and Faisal, are to be allocated to six tasks, \(1,2,3,4,5\) and 6 . The following table shows the tasks that each person is able to undertake.
PersonTask
Andy1,3
Bob1,4
Colin2,3
Dev\(4,5,6\)
Eric\(2,5,6\)
Faisal1,3
  1. Represent this information on a bipartite graph.
  2. Initially, Bob is allocated to task 1, Colin to task 3, Dev to task 5 and Eric to task 2. Demonstrate, by using an alternating path algorithm from this initial matching, how each person can be allocated to a different task.