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.)

Reference no: EM13919280

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