An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 23

The Clark County Shriff's Department schedules police officers for 8-hours 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 = the number of officers beginning work at 8:00 A.M., X 2 = the number of officers beginning work at noon, and so on.)