DSCI 5210 model bassed business intelligence question

The constraint for 10:00 am 2:00 pm is given as: O x2+x429 O x2+x329 0 None of the others OX3+X429 0 x1+x229 The Denton County Sheriff's Department schedules some police ofcers 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 ofcer 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 the shift anytime from midnight to noon or $300 for the entire shift if beginning the shift anytime from noon to midnight. During normal weekdayr operations. the number of part~time reserve ofcers needed varies depending on the time of the day. The department stafng guidelines require the following minimum number of part-time reserve ofcers on duty [see the table below}. The Denton County Sheriff's Department would like to formulate a linear program and determine the least expensive wayr that part'time reserve police ofcers could be scheduled to begin the Show 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 X1= the number of ofcers beginning work at 2:00 am, X2= the number of ofcers beginning work at 6:00 am, etc. Time of Day_ Minimum Ofcers 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 X3 + X52 11 is for: 0 None of the others 0 6:00 pm - 10:00 pm 0 1011) am - 2:00 pm 0 6:00 am - 10:00 am 0 1011) pm - 2:00 am Hiring 7 ofcers in each shift can be a feasible solution. 0 True 0 False