Jack Boyd can conduct various affairs from his office.
Jack Boyd can change his shift roll, hire new officers and fire officers here. You can check your backlog there as well.
Jack Boyd can make requests once a week at the city hall. He may request additional beat officer slots, detective slots, better SWAT gear (thus allowing the the SWAT to mobilize more than once a day or increasing their proficiency) and increase his own salary.
It can receive through the story as Jack replace Kendrick as a mole in the police station. Jack Boyd can exchange money for favors with the Sand Mafia. He may create a crime trap (that will kill all the officers sent out to the patrol, thus freeing up the slots), an investigation trap (killing a detective sent on the investigation, thus freeing up a slot) or intimidate the jury.
You receive it if you help Atticus to remove protesters who oppose the demolition of the park. Jack Boyd can buy favors from the Atticus Corporation. He may hold a house party to get 8 of his men to relax at a luxury house party, safely fire an employee by sending them to Atticus security detail, get Atticus Corp. to donate more money to the police force so he can have more officers/detectives and finally have his secret account where the money will be hidden from prosecutors.
You can receive it if you help the Bishop to remove some drug addicts outside of the church. Jack Boyd could have the church what people say it might be useless task: the bishop would bless the police station, forgive the police officers sins, the bishop would give an eulogy to the deceased police officers and detectives personally or by phone, pray for Jack's family, touch holy relics and give sermons to the police staff. Many people say it is a good place spend money for useless things. However, personally I think that the forgive sins can remove the alcohol problems.
The Labor Union
You can receive it if you help the Union Boss to ambush his assistant. Jack Boyd can look into his police officers and detectives' political views, fire his people illegally without getting trouble, remove municipal tasks completely and hire a snitch if you haven't done it with the deputy.