Without trying all 2,000! possible combinations of dorm room
assignments, we would like to find the combination where everyone is
the happiest. To do this we need a way to quantify how bad a
configuration is, that is, how unhappy the students are likely to
be. We define an objective function, 
, to capture as much knowledge
as possible regarding preferences and policy choices. Our goal is to
find the set of assignments with the smallest value of , thereby
minimizing mismatches.