The sheriff’s department schedules police officers for 8 hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:
Time of dayMinimum Officers on Duty
8:00 a.m. – noon 5
Noon – 4:00 p.m. 7
4:00 p.m. – 8:00 p.m.10
8:00 p.m. – midnight 8
Midnight – 4:00 a.m. 4
4:00 a.m. – 8:00 a.m. 6
Determine the number of police officers that should be scheduled to begin the 8 hour shifts at each of the six times to minimize the total number of officers required. Are there any surpluses? If so, during which shifts?
I just need help finding the constraints on this. I can't seem to work through this one in my head. Thanks.
Time of dayMinimum Officers on Duty
8:00 a.m. – noon 5
Noon – 4:00 p.m. 7
4:00 p.m. – 8:00 p.m.10
8:00 p.m. – midnight 8
Midnight – 4:00 a.m. 4
4:00 a.m. – 8:00 a.m. 6
Determine the number of police officers that should be scheduled to begin the 8 hour shifts at each of the six times to minimize the total number of officers required. Are there any surpluses? If so, during which shifts?
I just need help finding the constraints on this. I can't seem to work through this one in my head. Thanks.