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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 ofDay
MinimumOfficersonDuty
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.
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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