1 Answer this question on the insert provided. Mrs Price has bought six T shirts for her children. Each child is to have two shirts.
Amanda would like the green shirt, the pink shirt or the red shirt.
Ben would like the green shirt, the turquoise shirt, the white shirt or the yellow shirt.
Carrie would like the pink shirt, the white shirt or the yellow shirt.

1. On the first diagram in the insert, draw a bipartite graph to show which child would like which shirt. The children are represented as \(A 1 , A 2 , B 1 , B 2 , C 1\) and \(C 2\) and the shirts as \(G , P , R , T , W\) and \(Y\). Initially, Mrs Price puts aside the green shirt and the pink shirt for Amanda, the turquoise shirt and the white shirt for Ben and the yellow shirt for Carrie.
2. Show this incomplete matching on the second diagram in the insert.
3. Write down an alternating path consisting of three arcs to enable the matching to be improved. Use your alternating path to match the children to the shirts.
4. Amanda decides that she does not like the green shirt after all. Which shirts should each child have now?