^**Please give formulas and step by step instructions**^

A cosmopolitan area was deciding what form of security to use inits subway systems. The city ultimately decided to use metaldetectors at the entrance of the subway, but it still must hiresecurity personnel to patrol the area. The town currently uses bothcity police officers (P) and privately contracted security guards(G). The annual cost of one police officer is $65,000 in wages andbenefits, while security guards only cost the city $35,000 per yearon average. Each security guard reduces the number of muggings andviolent crimes by 2 annually and deters 25 free riders. However,because of their focus on more serious crimes, a police officeronly deters 15 free riders annually, but their presence prevents anestimated 6 muggings and violent crimes annually. The city mustdecrease muggings and violent crime by 250 incidents and reduce thenumber of free riders by 1,000. The town must have at least 12police officers dedicated to patrolling subways, and because of apreviously existing contract, they must employ at least 20 securityguards. The city’s objective is to meet these constraints with theleast cost combination. How many city police officers and privatelycontracted security guards should the city hire?