Calabrese City allocates some indirect or overhead costs to each of its police stations. The city charges each station for common services such as the city food service and for administrative services such as payroll. For the coming year, the Washington Square Police Station will have a total budget allocation of $1,400,000. That will be its only revenue. All direct and indirect charges have to be paid from that budgeted amount.
Each police station must pay $100,000 for processing its payroll. In addition, once arrests are made, the prisoners spend a day or two in the local police station, where the city must feed them. On average, the City Food Service charges each police station $40 for meal service for each arrest.
The station would like to maximize its number of arrests to reduce the cumber of criminals on the street. However, more arrests require not only more food, but also more police officers.
The personnel employed by the Washington Square Station are supervisors, desk clerks, and police officers. The minimum staffing levels based on total budgeted arrests are as follows:
Annual Number of Arrests Police Officers Desk Clerks Supervisors
0-1,000 11 6 2
1,001-2,000 12 6 2
2,001-3,000 12 7 2
3,001-4,000 13 8 3
Annual salaries for each class of employee follow: supervising officers, $68,500; desk clerks, $59,000; and police officers, $54,000. Note that this police station cannot process more than 4,000 arrests per year.
Calculate the maximum number of arrests that Washington Square can budget and still expect to break even for the coming year.