LP Formulation
Let xij = 1 if swimmer i swims event j and 0 otherwise
MIN 5.88 X15 + 6.91 X16 + 9.1 X17 + 7.36 X18 + 9.3 X25 + 6.53 X26
+ 7.62 X27 + 3.28 X28 + 8.46 X35 + 4.16 X36 + 2.62 X37 + 6.23 X38
+ 5.27 X45 + 7.01 X46 + 2.47 X47 + 7.56 X48
2) X15 + X16 + X17 + X18 = 1 ! John = swimmer 1
3) X25 + X26 + X27 + X28 = 1 ! Paul = swimmer 2
4) X35 + X36 + X37 + X38 = 1 ! George = swimmer 3
5) X45 + X46 + X47 + X48 = 1 ! Ringo = swimmer 3
6) - X15 - X25 - X35 - X45 = - 1 ! Freestyle = event 1
7) - X16 - X26 - X36 - X46 = - 1 ! Butterfly = event 2
8) - X17 - X27 - X37 - X47 = - 1 ! Backstroke = event 3
9) - X18 - X28 - X38 - X48 = - 1 ! Breaststroke = event 4
0 <= Xij <= 1 for all (i,j)