Formulate and solve the nurse scheduling problem as an integer program for one day for the data given below.

Hospital administrators must schedule nurses so that the hospital’s patients are provided adequate care. At the same time, careful attention must be paid to keeping costs down. From historical records, administrators can project the minimum number of nurses required to be on hand for various times of day and days of the week. The objective is to find the minimum total number of nurses required to provide adequate care. Nurses start work at the beginning of one of the four-hour shifts given below (except for shift 6) and work for 8 consecutive hours. Hence, possible start times are the start of shifts 1 through 5. Also, assume that the projected required number of nurses factors in time for each nurse to have a meal break. Formulate and solve the nurse scheduling problem as an integer program for one day for the data given below. Hint: Note that exceeding the minimum number of needed nurses in each shift is acceptable so long as the total number of nurses over all shifts is minimized.

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