The medley relay requires four swimmers to each swim a different stroke: butterf
ID: 415127 • Letter: T
Question
The medley relay requires four swimmers to each swim a different stroke: butterfly, breaststroke, backstroke, and freestyle. The relay is the final event in the competitions, and the outcome of the swim meet often depends on the performance of the relay team. During practice, coach Mandrik has asked each of his top four swimm ers to try each of the four strokes, and he has tracked their times (in seconds), as shown in the table below.
Stroke Tim (T) Ben (B) Leah (L) Cindy (C) Butterfly(1) Breaststroke(2) Backstroke(3) 75 76 71 80 38 34 41 43 41 45 Freestyle(4) 27 25 26 30Explanation / Answer
Time matrix 1 2 3 4 T 38 75 44 27 B 34 76 43 25 L 41 71 41 26 C 33 80 45 30 Assignment matrix 1 2 3 4 T 0 0 1 0 B 0 0 0 1 L 0 1 0 0 C 1 0 0 0 Constraints All swimmers should use only one stroke T 1 = 1 Sum of row across a row should be 1 B 1 = 1 Sum of row across a row should be 1 L 1 = 1 Sum of row across a row should be 1 C 1 = 1 Sum of row across a row should be 1 All Strokes should be used by one swimmer 1 1 = 1 Sum of column across a stroke should be 1 2 1 = 1 Sum of column across a stroke should be 1 3 1 = 1 Sum of column across a stroke should be 1 4 1 = 1 Sum of column across a stroke should be 1 This is clear case of assignment problem hence all the assignment variables should be binary Objective function Minimize total time 173 sumproduct of time matrix and assignment matrix Solved using solver So the final optimal assignment is T-3 B-4 L-2 C-1 And optimal time is 173