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The Clark County Sheriffs Department schedules police officers for 8-hour shifts. The beginning times for...

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Finance

The Clark County Sheriffs 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 No. of Officers on Duty
8:00 a.m.noon 7
Noon4:00 p.m. 6
4:00 p.m.8:00 p.m. 7
8:00 p.m.midnight 7
Midnight4:00 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 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.) If your answer is zero, enter 0.

Starting Time Officers Starting
8:00 a.m.
Noon
4:00 p.m.
8:00 p.m.
Midnight
4:00 a.m.

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