[2.5 points] during each 4-hour period, the smalltown police force requires the following number of on-duty police officers: 8 officers from 12 midnight to 4am; 7 officers from 4am to 8am; 6 officers from 8am to 12 noon; 6 officers from 12 noon to 4 pm; 5 officers from 4 to 8pm and 4 officers from 8pm to 12 midnight. each officer works two consecutive 4-hour shifts. formulate an ilp that can be used to minimize the number of police officers needed to meet smalltown’s daily requirements. write down your mathematical models. use excel or gams to solve the problem, and print out your excel or gams codes and solution.