a) For this question only, X = 1109. There are X pounds of food on an island that must be allocated between 2 marooned sailors.

The utility function of the first sailor is given by: = 1 2 1 Where F1 is the quantity of food consumed by the first sailor.

For the second sailor, utility (as a function of food consumption) is given by: = 1 3 2

i) If the food is allocated equally between the sailors, how much utility will the second sailor receive? [1 mark]

ii) How should the food be allocated between the sailors to ensure that they are both equally satisfied? [2 marks]

iii) Suppose that the second sailor requires a utility level of at least 5 to remain alive. How much food should be allocated to the first sailor to maximize the sum of utilities while ensuring that the second sailor remains alive? [2 marks]