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: 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.)
The Clark County Sheriff’s Department
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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