Question 9 (14 marks) In February 2010 a pair of siblings in Melbourne were contacted by a lawyer informing them that one of their distant relatives had passed away and left them her estate. The will did not specify how the estate was to be divided between the siblings, and so the siblings decided to use a method they learnt in DMOR class, the Adjusted Winner Method, in order to divide everything in the fairest possible way. They came up with the following point allocations for the items. 22 Item 1 Apartment in Brunswick 2 Vintage car 3 Large household items 4 Jewellery 5 Concert piano 6 Flat screen TV 7 Art works 8 Family photos 9 Small household items 10 Misc. items Sibling 1 Sibling 2 9 22 15 15 15 14 3 11 15 6 5 11 2 7 2 7 2 13 (a) Use the Adjusted Winner method to determine which items each sibling will inherit. Suppose that ties are broken in favour of Sibling 1. (b) Prove that the allocation is envy free and equitable