Consider the case were we only use 12-hour nurses over a 4-week (28-day) horizon. In this case, we have m nurses on our roster, which we will pay regardless of assignment. We no longer have the restriction of 3-days on followed by 4-days off. Develop a formulation where our hard constraints are that we meet demand for both shifts each day and that a nurse can't work two shifts in a row. We would like to use two goals (soft constraints): i) Nurses get at least 2 weekend days off over the month, and ii) Nurses would like to work exactly 16 days over the month. Clearly define your decision variables (and use Di for demand for day shift on day i and Ni as demand for night shift on day i). You only need to formulate this.

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