The Denton County Fire Department schedules some firefighters 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. A firefighter 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 firefighters needed varies depending on the time of the day. The department staffing guidelines require the following minimum number of fighters on duty (see the table below). The Denton County Fire Department would like to formulate a linear program and determine the least expensive way that firefighters 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 fighters beginning work at 2:00 am, X the number of firefighters beginning work at 6:00 am, etc. Time of Day Minimum Fighters Required on Duty 2:00 am-6:00 am 8 6:00 am -10:00 am 15 10:00 am 2:00 pm 12 2:00 pm - 6:00 pm 6:00 pm - 10:00 pm 15 10:00 pm-2:00 am 11 The constraint for 2:00 am - 6:00 am is given as: OX4+X58 OX1+X28 None of the others OX1+X68 OX3 X48 The constraint X5 +X6 15 is for: O 10:00 pm-2:00 am O 10:00 am-2:00 pm O 6:00 am 10:00 am O None of the others O 6:00 pm 10:00 pm Hiring 8 firefighters each shift is a feasible solution. O True O False