For the 8-hour day shift in a hospital emergency room, the number of nurses needed, by day, is as follows:

All day-shift nurses work five 8-hour shifts per week and are entitled to two consecutive days off per week. Management would like to know a) the minimum number of nurses needed to provide the above capacity each day. (b) What will be the actual capacity by day? (c) What days will each nurse work?

Tour 1 = Tuesday to Saturday. Tour 2 = Wednesday to Sunday. Tour 3 = Thursday to Monday. Tour 4 = Friday to Tuesday.Tour 5 = Saturday to Wednesday. Tour 6 = Sunday to Thursday. Tour 7 = Monday to Friday.

Recall the nurse-scheduling problem (with full-time nurses only) introduced in class. We now know that this staffing plan cannot be achieved with fewer than 8 nurses. However, nurses prefer to work tour 7 because the days off are Saturday and Sunday. Nurses also like tours 1 and 6 because one day off is a Saturday or Sunday, respectively. Reformulate the problem so that it uses exactly 8 nurses but the number of nurses assigned to tours 1, 6 and 7 is maximized while meeting minimum daily staffing needs. How did you reformulate the decision variables, objective function and constraints?