Suppose you are the police chief. You are about to employ 10 new police officers. Some of these officers you will put on bike theft duty and the others on homicide. A value to society of capturing a murder is $10,000. The benefit to society of preventing a bike theft is $400. The cost of placing a cop on homicide is $1,000 (additional training). The cost of placing a cop on bike theft is $100. Adding a police officer to homicide increases the likelihood of capturing a murder by .2*(number of homicide police)0.5. Each additional cop of bike duty guarantees a prevented bike theft. How many officers do you allocate to homicide and to bike theft?