The coach of an age group swim team needs to assign swimmers to a 200-yard med

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 each of the four strokes. The five fastest swimmers and the best
time (in seconds) they have achieved in each 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 determine how to assign four swimmers to the four different strokes to minimize the sum of the corresponding best times.

a.) Fomulate this problem as an assignment problem.

b.) Obtain an optimal solution.