The Hilton Island Tennis Club is hosting its annual professional tennis tournament. One of the tournament committee’s scheduling activities is to assign chair umpires to the various matches.

The tennis association rates chair umpires from 1 (best) to worst (4) based on experience, consistency, and player and coach evaluations. On a particular afternoon 12 matches start at 1:00 p.m.

Fifteen chair umpires are available to officiate the matches. The matches are prioritized from 1 to 12 in order of importance, based on the rankings and seedings of the players involved, and whether it is a singles or a doubles match. The committee wants to assign the best umpires to the highest priority matches. The following tables show the match priorities and the umpire ratings.

Umpire 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Rating 3 4 3 1 2 2 3 2 4 4 2 1 4 3 3 Match 1 2 3 4 5 6 7 8 9 10 11 12 Priority 2 11 6 4 9 10 12 3 1 5 7 8 Determine the optimal assignment of umpires to matches.