1. Solve the problem using the Hungarian Method. (6 points)
2. If Ken was removed from the candidate swimmers list, how would the solution change? If necessary, solve again using the Hungarian Method. (4 points)

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 their best times (in seconds) they have achieved in each of the strokes (for 50 yards) are Backstroke Breaststroke Butterfly Freestyle Carl 37.7 43.4 33.3 Chris 32.9 33.1 28.5 26.4 David 33.8 42.2 38.9 29.6 Tony 37.0 34.7 30.4 28.5 29.2 Ken 35.4 41.8 33.6 31.1 Now consider the following formulation for this assignment problem: Sets: Swimmers, i = Carl, Chris, David, Tony, Ken Stroke style, j = Backstroke, Breaststroke, Butterfly, Freestyle Variables:Xij: 1, if swimmer i is assigned to stroke style j; 0, if not Parameters:Cij: Fastest time of swimmer i using stroke style j Minimize Z= CijXij Subject to Vj = 1 xuj = 1 Vi Xij = {0,1} Vij Xu 20 Vi