The Clark County 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:
Minimum Officers
Time of Day On Duty
8:00 A.M.–Noon .......... 5
Noon–4:00 P.M. .......... 6
4:00 P.M.–8:00 P.M. ......... 10
8:00 P.M.–Midnight ............. 7
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 (8:00 A.M., noon, 4:00 P.M., 8:00 P.M., midnight, and 4:00 A.M.) to minimize the total number of officers required. (Let x1 = the number of officers beginning work at 8:00 A.M., x2 = the number of officers beginning work at noon, and so on.)