Question 7 Start on a new page. Total marks = 5. The coach of a swimming team needs to assign swimmers to a 200-meter medley relay team to be sent 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 fours strokes. The five fastest swimmers and the best times (in second) they have achieved in each of the strokes (for 50 meters) are: Stroke Backstroke Breaststroke Butterfly Freestyle Carl 37.7 43.4 33.3 29.2 Chris 32.9 33.1 28.5 26.4 Swimmer David 33.8 42.2 38.9 29.6 Tony 37.0 34.7 30.4 28.5 Ken 35.4 41.8 33.6 31.1 The coach wishes to determine how to assign four swimmers to four different strokes to minimize the sum of the corresponding best times. (a) (b) Obtain an optimal solution. Which swimmer will not be sent by the coach for this relay competition? [4+1 = 5 marks] Question 7 Start on a new page. Total marks = 5. The coach of a swimming team needs to assign swimmers to a 200-meter medley relay team to be sent 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 fours strokes. The five fastest swimmers and the best times (in second) they have achieved in each of the strokes (for 50 meters) are: Stroke Backstroke Breaststroke Butterfly Freestyle Carl 37.7 43.4 33.3 29.2 Chris 32.9 33.1 28.5 26.4 Swimmer David 33.8 42.2 38.9 29.6 Tony 37.0 34.7 30.4 28.5 Ken 35.4 41.8 33.6 31.1 The coach wishes to determine how to assign four swimmers to four different strokes to minimize the sum of the corresponding best times. (a) (b) Obtain an optimal solution. Which swimmer will not be sent by the coach for this relay competition? [4+1 = 5 marks]