Full time police officers in a small town work twelve hour shifts, beginning at midnight, 3a, noon, 6p, or 9p. Since crime and traffic depend on the time of day, so does the minimum number of officers needed as shown in table below. Officers will take a 3 hour break after 6 hours of work. Constables earn a base rate of $45 per hour, but are paid a bonus of $9 per hour when working from midnight to 6 a.m, even when they are on break. Part time officers are used to cover the busy part of the day. Part time officers work 6hours and can start at 9a, noon or 3p. They are paid $30 per hour. Formulate an LP model to help theTown determine how many officers should be assigned to each shift to minimize total cost. Solve themodel using LINGO. How many full-time officers will be needed? What is the total cost for part time officers?

 

Time Required 195 00-03 03-06 100 06-09 09-12 12-15 15-18 18-21 160 110 115 135 21-24 120 160