AQA D1 2010 January — Question 1

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2010
SessionJanuary
TopicMatchings and Allocation

1 Six girls, Alfonsa (A), Bianca (B), Claudia (C), Desiree (D), Erika (E) and Flavia (F), are going to a pizza restaurant. The restaurant provides a special menu of six different pizzas: Margherita (M), Neapolitana (N), Pepperoni (P), Romana (R), Stagioni (S) and Viennese (V). The table shows the pizzas that each girl likes.
GirlPizza
Alfonsa (A)Margherita (M), Pepperoni (P), Stagioni (S)
Bianca (B)Neapolitana (N), Romana (R)
Claudia (C)Neapolitana (N), Viennese (V)
Desiree (D)Romana (R), Stagioni (S)
Erika (E)Pepperoni (P), Stagioni (S), Viennese (V)
Flavia (F)Romana (R)
  1. Show this information on a bipartite graph.
  2. Each girl is to eat a different pizza. Initially, the waiter brings six different pizzas and gives Alfonsa the Pepperoni, Bianca the Romana, Claudia the Neapolitana and Erika the Stagioni. The other two pizzas are put in the middle of the table. From this initial matching, use the maximum matching algorithm to obtain a complete matching so that every girl gets a pizza that she likes. List your complete matching.