During each 4-hour period, the Smalltown police force requires the following number of on-duty police officers: 8 from midnight to 4 a.m.; 7 from 4 a.m. to 8 a.m.; 6 from 8 a.m. to noon; 6 from noon to 4 p.m.; 5 from 4 p.m. to 8 p.m.; and 4 from 8 p.m. to midnight. Police officers can be scheduled to work either 8-hour shifts or 12-hour shifts. To accommodate personal preferences, at least 45% of the police officers must be scheduled to work 8-hour shifts. Determine how to minimize the number of police officers needed to meet Smalltown’s daily requirements. Total number of police officers =
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Keondre P.
During each 4-hour period, the Smalltown police force requires the following number of on-duty police officers: 12 midnight to 4 A.M.—8; 4 to 8 A.M.—7; 8 A.M. to 12 noon—6; 12 noon to 4 P.M.—6; 4 to 8 P.M.—5; 8 P.M. to 12 midnight—4. Each police officer works two consecutive 4-hour shifts. Formulate an LP that can be used to minimize the number of police officers needed to meet Smalltown’s daily requirements.
Jon S.
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 No. of Officers on Duty 8:00 a.m. - noon 5 Noon - 4:00 p.m. 6 4:00 p.m. - 8:00 p.m. 8 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 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.
Sri K.
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