Q. The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to every of the four strokes. The five fastest swimmers also the best times (in seconds) they have achieved in every of the strokes (for 50 yards) are
Stroke Carl Chris David Tony Ken
Backstroke 37.7 32.9 33.8 37.0 35.4
Breaststroke 43.4 33.1 42.2 34.7 41.8
Butterfly 33.3 28.5 38.9 30.4 33.6
Freestyle 29.2 26.4 29.6 28.5 31.1

The coach wishes to Conclude how to assign four swimmers to the four different strokes to minimize the sum of the corresponding best times.

(a) Formulate this trouble as an assignment trouble.

(b) Obtain an optimal solution.