Interesting problem, though I think that no AI or genetic algorith will give you the optimal solution.
It could be done as a linear programming case (as already stated), but it would be easier to just do a brute force type of search - i.e., test all the possible combinations for the optimal schedule. This is not an elegent approach, but it will work, and I doubt you have enough variables to make your pc choke.
If you want just a "good" and not necessarily and the optimal solution, you could evolve something pretty easily.
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