Chris Pearson is running a tennis tournament and is in the process of scheduling the umpires for each match in today’s rounds. There are five matches to be played today, and there are six umpires available. Every match needs exactly one umpire and no umpire can be assigned to more than one match. The following table shows the number of times (in the past) that each umpire has been scheduled for a match involving one of the competing players in each of the matches. Chris wants to assign umpires to matches in a way that avoids placing umpires with players they have seen many times.

a. Chris has decided to minimize the sum of the number of times the umpires have previously been paired with the players. What is the optimal assignment of umpires to matches?
b. Suppose Chris were to apply a weighting factor to the assignments, treating the assignments in the three singles matches as if they counted double the other assignments. Does this change the optimal assignments?