Question

The minimum staffing levels based on total budgeted arrests are as follows:

Annual # of Arrests	Police Officers	Desk Clerks	Supervisors
0-1000	11	6	2
1001,-2000	12	6	2
2,001-3,000	12	7	2
3,001-4000	13	8	3

C 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 C 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 of its payroll. In addition, once arrests are made, the prisoners spend a day or two at the local police station, where the city must feed them. On average, the city food service charges each police station $40 for the meal service for each arrest.

The statiion would like to maximize its number of arrests to reduce the number of criminals on the street. However, more arrests require not only mood food, but also more police officers.

Annual salaries for each class are as follows:

Police Officers: $54,000

Desk Clerks: $59,000

Supervising Officers: $68,500

*Note that this police station cannot process more than 4,000 arrests per year due to size.

Calculate the surplus or deficit at each maximum annual number of arrests staffing levels (1000,2000,3000,4000). Calculate the maximum number of arrests that C Police Station can budget for and still expect to break even for the coming year. (Hint; Once you have found the range of annual arrests that the C Police Station from a surplus to a deficit, focus on what costs are variable between those two levels to find the exact BEQ).

Demonstrate these calculations in a steo-by-step procedure.

Answer 1

As given in the question the budget is of $1,400,000

therefore for us to calculate the maximum number of number of arrest the police station C could made we need to following steps:

1. we need to remove all the fixed cost that are to be paid no matter what i.e. processing payroll charges of $100,000.

2. therefore we now have of $ 1,300,000. Now we need to deduct charges for all the police officers, clerks and of supervising officers at different level of arrest.

3. Now we will deduct total cost from budgeted amt left after deducting payroll charges.

For 0-1000 total cost is $1085000 that we will deduct from $1,300,000 that will be $ 215000 will be still left for the paying $40 for each arrest meals charges the arrest we colud make in that is $215000\40= 5375 arrest we could make that is above the range as well as the station capacity

4. Instead that we will select the range 2001-3000 and the total cost for this is as given in the image is $1198000

that we will deduct from our remmaing budgeted cost of $1,300,000 the answer will be $102,000 remmaing for the meal charges of $40 each arrest therefore the number of arrest that could me made would be $102000\40=2550 arrest and the number of arrest are within the range and at 2550 areest there will be not be any defecit for the police station.

5. If they go any higher there will be defecit for the police station.

6. Therefore the maximum arrest the C police station could make will be of 2550 criminals and that will be the Break even point for the police station C.