- The Next Three Questions Refer To The Following Case The Denton County Sheriff S Department Schedules Some Police Offic 1 (160.39 KiB) Viewed 31 times
The next three
questions refer to the following case: The Denton County Sheriff's Department schedules some police officers for 8- hour shifts. The beginning times for the shifts are 3:00 am, 7:00 am, 11:00 am, 3:00 pm, 7:00 pm and 11:00 pm. An officer beginning a shift at one of these times works for the next 8 hours and he/she is paid $300 for the entire shift if beginning the shift anytime from midnight to noon or $360 for the entire shift if beginning the shift anytime from noon to midnight. During normal weekday operations, the number of part-time reserve officers needed varies depending on the time of the day. The department staffing guidelines require the following minimum number of part-time reserve officers on duty (see the table below). The Denton County Sheriff's Department would like to formulate a linear program and determine the least expensive way that part-time reserve police officers could be scheduled to begin the 8-hour shifts at each of the six times (3:00 am, 7:00 am, 11:00 am, 3:00 pm, 7:00 pm and 11:00 pm). Let X₁= the number of officers beginning work at 3:00 am, X₂= the number of officers beginning work at 7:00 am, and so on.
Time of Day 3:00 am - 7:00 am 8 7:00 am - 11:00 am 16 11:00 am - 3:00 pm Minimum Officers on Duty. 7:00 pm - 11:00 pm 3:00 pm - 7:00 pm 14 11:00 pm - 3:00 am 12 18 22
The constraint X3 + X4 ≥ 14 is for: 3:00 pm - 7:00 pm None of the other options. O 7:00 pm - 11:00 pm 11:00 am - 3:00 pm 11:00 pm - 3:00 am
The constraint for 3:00 am - 7:00 am is given as: X1 + X2 ≥ 8 X1 + X6 ≥ 18 X1 + X2 ≥ 8 O None of the other options. X1 ≥ 8
Hiring 51 officers in total across the 6 shifts can be a feasible solution. True False