Question: Nurses at a large hospital in Dallas work three-day schedules and receive a weekly wage according the table below. For example, a nurse working schedule type 1 works Monday, Tuesday, and Sunday, and receives a weekly wage of $525; a nurse working schedule type 5 works Tuesday, Thursday, and Friday, and receives a weekly wage of $425. The number of nurses required at the hospital each day is given in the right-most column of the table; for example, there must be at least 20 nurses working on Monday and at least 25 working on Tuesday.

1. Formulate an appropriate mathematical programming model to determine the number of nurses to hire for each schedule type so that the daily demands for nurses at the hospital are met at minimum total cost.
2. How does your formulation from part (a) change if part-time nurses can be hired to work for $150 per day?
3. How does your formulation from part (b) change if for each part-time nurse working on any day there must be at least four regular-time nurses (nurses who work schedule type 1, 2, 3, 4, or 5) working at the same time?

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