The medley relay requires four swimmers to each swim a different stroke: butterf
ID: 414765 • 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
1 2 3 4 T 38 75 44 27 B 34 76 43 25 L 41 71 41 26 C 33 80 45 30 Decision variable matrix with values 0 or 1 1 in any box means that stroke will be by that swimmer, and 0 means he is not using that stroke 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 Each swimmer can have only one type of stroke T 1 = 1 (1 here means each swimmer is using only one stroke) B 1 = 1 (1 here means each swimmer is using only one stroke) L 1 = 1 (1 here means each swimmer is using only one stroke) C 1 = 1 (1 here means each swimmer is using only one stroke) Each swimmer should have a different stroke 1 1 = 1 (1 here means each stroke is used by only one swimmer) 2 1 = 1 (1 here means each stroke is used by only one swimmer) 3 1 = 1 (1 here means each stroke is used by only one swimmer) 4 1 = 1 (1 here means each stroke is used by only one swimmer) Objective function Minimize total swim time 173 sumproduct of decision variable matrix and time matrix So basis solver solution the solution is T-3 B-4 L-2 C-1 And the minimum time taken is 173