Relay Optimizing Algorithm

A team of eight swimmers wants two enter two 4x100meter medley relays in a swim meet.  (The medley relay consists of one leg butterfly, one leg backstroke, one leg breaststroke, one leg freestyle.) Each swimmer can do all four strokes.

A) Develop an algorithm to find the fastest single relay.  (One person might have the fastest times in all four strokes).

B) Keeping in mind that one swimmer can do only one leg, and that all four legs of both relays must be filled, devise an algorithm to allocate the swimmers so that the two relays have the lowest possible cumulative time.

(Alternatively generalize the solution for 4n swimmers swimming n relays.  This isn't for homework, just wondering what ppl would do.)

TOO MUCH TEXT, WHAT'S THE MATH?

Solution:
1. Feed constraints into constraints solver.
2. Solve.

Exhaustive search 4 teh win.

Dynamic programming?

Ok then, giving an m x n matrix such that m >> n, how do I create a vector whose entries have the smallest sum possible, such that at most one entry is taken from each column in the matrix?

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Marijuana MUST be legalized.