Hatfield and McCoy Burn with Hatred for Each Other

Multiple Choice

Hatfield and McCoy burn with hatred for each other.They both consume corn whisky.Hatfield's utility function is U = W_H - W ²_M /8 and McCoy's utility is U = W_M - W ²_H /8, where W_H is Hatfield's whisky consumption and W_M is McCoy's whisky consumption, measured in gallons.The sheriff has a total of 48 gallons of confiscated whisky which he could give back to them.For some reason, the sheriff wants them both to be as happy as possible and he wants to treat them equally.The sheriff should give them each

A) 24 gallons.
B) 2 gallons and spill 44 gallons in the creek.
C) 4 gallons and spill 40 gallons in the creek.
D) 8 gallons and spill the rest in the creek.
E) 1 gallon and spill the rest in the creek.