Fire department staffing optimization
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A fire department says that they must have full time firemen work on different days of the week. They must have 10 on mon, 11 on tues, 12 on wed, 13 on thurs, 14 on fri, 15 on sat and 16 on sun. Each fireman must work 5 (any 5) consecutive days and then have two days off. but sometimes they can work one day a week OT. each fireman is paid $100/day regular pay and if they work OT they get $125/day.
I need to minimize the cost of meeting the requirements above. The next constraint is that they can each only work one day OT. So if they work mon, tues, wed, thurs, fri, they could if needed work either sat OR sun. How do I set this up?
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