### Determine number of police officers that should be scheduled

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##### Reference no: EM13919280

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 num- ber of officers on duty:

 Time of Day Minimum Officers 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. (Hint: 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.)

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