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 no clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the bes times (in seconds) they have achieved in each of the strokes (for 50 yards) are Stroke Backstroke Breaststroke Butterfly Freestyle Carl 37.7 43.4 33.3 29.2 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 Ken 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.
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 no clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the bes times (in seconds) they have achieved in each of the strokes (for 50 yards) are Stroke Backstroke Breaststroke Butterfly Freestyle Carl 37.7 43.4 33.3 29.2 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 Ken 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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
Stroke
Backstroke
Breaststroke
Butterfly
Freestyle
Carl
37.7
43.4
33.3
29.2
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
Ken
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.
(c) Apply the Hungarian method to obtain an optimal solution.
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