- Six workers \(A , B , C , D , E\) and \(F\) are to be matched to six tasks \(1,2,3,4,5\) and 6 .
The table below shows the tasks that each worker is able to do.
| Worker | Tasks |
| \(A\) | \(2,3,5\) |
| \(B\) | \(1,3,4,5\) |
| \(C\) | 2 |
| \(D\) | 3,6 |
| \(E\) | \(2,4,5\) |
| \(F\) | 1 |
A bipartite graph showing this information is drawn in the answer booklet.
Initially, \(A , B , D\) and \(E\) are allocated to tasks 2, 1, 3 and 5 respectively.
Starting from the given initial matching, use the matching improvement algorithm to find a complete matching, showing your alternating paths clearly.
(5)