Question

The Clark County Sheriff's Department schedules police officers for 8-hour 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: Time of Day Minimum No. of Officers on Duty 8:00 a.m.-noon 7 Noon-4:00 p.m. 6 4:00 p.m.-8:00 p.m. 7 8:00 p.m.-midnight 7 Midnight-4:00 a.m. 4 4:00 a.m.-8:00 a.m. 6 Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. (Hint: Let x1 = the number of officers beginning work at 8:00 a.m., x2 = the number of officers beginning work at noon, and so on.) If your answer is zero, enter "O". Starting Time Officers Starting 8:00 a.m. 5 Noon 1 4:00 p.m. 9 8:00 p.m. -2 Midnight 6 4:00 a.m. 0

Answer 1

DATE:30-07-2020

ANSWER:---------

solution A linear program model is a mathematical model with a linear objective function and a set of linear constrains, and non-negative variables. let. Si be the no-of officers scheduled ato-8.a.m. So be the no. of officers scheduled at - noon Sa be the no.of officers scheduled at a Upm. Su be the no of officers scheduled at -8pm. Ss be the noot afficers secheduled at - midnight So be the no of officers scheduled at - 4am. CS Scanner with Camscanner

OUTPUT: SiS S₃ S4 S5 S6 USED Available 0 7 7 - o 6 01017 0 0> 6 1 1 7 WWWWW O o - O 0 7 7 0 0 - 0 0 0 6 -- 6. objective function 60 7 O 5 1 Z 1 Minimum 19 2) Minimum = 6 +0+7+o+st! 2. = 19. Answer 6 7 0 5 CS Scanned with CamScanne

Answer 2