The Denton County Sheriff's Department schedules some police officers for 8-hour shifts. The beginning times for the shifts are 2:00 am, 6.00 am, 10:00 am, 2:00 pm, 6:00 pm and 10:00 pm. An officer beginning a shift at one of these times works for the next 8 hours and he/she is paid $240 for the entire shift if beginning th shift anytime from midnight to noon or $300 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 o 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 (2:00 am, 6:00 am, 10:00 am, 2:00 pm, 6:00 pm and 10:00 pm). Let X- the number of officers beginning work at 2:00 am, X the number of officers beginning work at 6:00 am, etc. Time of Day Minimum Officers on Duty 2:00 am - 6:00 am 8 6:00 am -10:00 am 11 10:00 am - 2:00 pm 9 2:00 pm - 6:00 pm 7 6:00 pm - 10:00 pm 11 10:00 pm - 2:00 am 13 The constraint X+ Xg 2 11 is for: O None of the others O 6.00 pm - 10:00 pm O 10:00 am - 2:00 pm O 6:00 am - 10:00 am O 10:00 pm - 2:00 am The constraint for 10:00 am - 2:00 pm is given as: O X2+ X4 9 O X2 + X3 29 O None of the others O X3 + X49 O X1 + X229 Hiring 7 officers in each shift can be a feasible solution. O True O False

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