There are 200 pounds of food on an island that must be allocated between 2 marooned sailors. The utility function of the first sailor is given by
Utility = √F1
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
Utility = ½ √F2
a. If the food is allocated equally between the sailors, how much utility will each receive?
b. How should food be allocated between the sailors to ensure equality of utility?
c. Suppose that the second sailor requires a utility level of at least 5 to remain alive. How should food be allocated to maximize the sum of utilities subject to the restraint that the second sailor receives that minimum level of utility?
d. What other criteria might you use to allocate the available food between the sailors?