Essentials of Business Analytics 1st Edition by Jeffrey Camm,James Cochran,Michael Fry,Jeffrey Ohlmann ,David Anderson

Exercise 3

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:

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 x 1 5 the number of officers beginning work at 8:00 a.m., x 2 5 the number of officers beginning work at noon, and so on.)