Atlantic Jail requires a staff of at least one guard for every four prisoners. The jail will hold 48 prisoners. Atlantic has a beach that attracts numerous tourists and transients in the spring and summer. However, the region is rather sedate in the fall and winter. The fall/winter population of the jail is generally between 12 and 16 prisoners. The numbers in the spring and summer can fluctuate from 12 to 48, depending on the weather, among other factors (including phases of the moon, according to some longtime residents).

Atlantic has four permanent guards hired on a year-round basis at an annual salary of $36,000 each. When additional guards are needed, they are hired-on a weekly basis at a rate of $600 per week. (For simplicity, assume that each month has exactly four weeks.)

1. Prepare a graph with the weekly planned cost of jail guards on the vertical axis and the number of prisoners’on the horizontal axis.

2. What would be the amount planned for jail guards for the month of January? Would this be a fixed cost or a variable cost?

3. Suppose the jail population of each of the four weeks in July was 25, 38, 26, and 43, respectively. The actual amount paid for jail guards in June was $19,800. Prepare a report comparing the actual amount paid for jail guards with the amount that would be expected with efficient scheduling and hiring.

4. Suppose Atlantic treated jail-guard salaries for nonpermanent guards as a variable expense of $150 per week per prisoner. This variable cost was applied to the number of prisoners in excess of 16. Therefore, the weekly cost function was weekly jail-guard cost = $3,000 + $150 x (total prisoners — 16)

Explain how this cost function was determined.

5. Prepare a report similar to that in step 3 above except that the cost function in step 4 should be used to calculate the expected amount of jail-guard salaries. Which report, this one or the one in step 3, is more accurate? Is accuracy the only concern?