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 times (in seconds) they have achieved in each of the strokes (for 50 yards) are Carl Chris David Ken Stroke Backstroke Breaststroke Butterfly Freestyle 37.7 43.4 33.3 29.2 32.9 33.1 28.5 26.4 33.8 42.2 38.9 29.6 Tony 37.0 34.7 30.4 28.5 35.4 41.8 33.6 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) Initialize this problem by adding the required dummy job person for the assignment problem. (b) Write an integer) linear programming formulation for the assignment problem. ©) Apply the Hungarian method to obtain an optimal solution.
