6. Van Nostrand Hospital must schedule nurses so that the hospital’s patients are provided with adequate care. At the same time, in the face of tighter competition in the health care industry, careful attention must be paid to keeping costs down. From historical records, administrators can project the minimum number of nurses to have on hand for the various times of day and days of the week. The nurse-scheduling problem seeks to find the minimum total number of nurses required to provide adequate care. Nurses start work at the beginning of one of the 4-hour shifts given next and work for 8 hours. Formulate and solve the nurse-scheduling problem as an integer program for one day for the given data.

Shift Time Minimum Number of Nurses Needed 1 12:00 A.M.–4:00 A.M. 5 2 4:00 A.M.–8:00 A.M. 12 3 8:00 A.M.–12:00 P.M. 14 4 12:00 P.M.–4:00 P.M. 8 5 4:00 P.M.–8:00 P.M. 14 6 8:00 P.M.–12:00 A.M. 10