Question

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

Answer 1

Answer:

a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.

b) applying the Hungarian method.

   4.8      0     0.9     4.1     2.5

   10.3     0     9.1      1.6     8.7

   4.8      0     10.4    1.9     5.1

   2.8      0     3.2     2.1     4.7

      0      0      0        0       0  

Deduct the smallest element in each column from the other elements of the column.

   2      0     0       2.5    0

   7.5   0     8.2    0       6.2

   2      0     9.5    0.3    2.6

   0      0     2.3    0.5    2.2

   0      0     0       0       0  

Which implies:      

   2            8.2    2.5    6.2

   7.5         9.5    0.3    2.6

   2            2.3    0.5    2.2

33.8 + 34.7 + 28.5 + 29.2 = 126.2

David = Back Stroke

tony = Breast Stroke

Chris = Butterfly

Carl = Free Style