Question

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

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

Answer 1

Hence, the city should employ 35 city police officers and 20 security guards in order to meet the required minimum demands.