The Overloaded Evidence Locker
You are a newly assigned case agent in a field office. The office has a single evidence locker room with 12 lockers, each holding up to 5 boxes. Currently, 9 lockers are full (5 boxes each), 2 lockers have 3 boxes each, and 1 locker is empty. Evidence from a major drug bust arrives: 8 new boxes. Simultaneously, you learn that 3 boxes in locker #4 are scheduled for destruction next week, and 2 boxes in locker #7 are overdue for return to the courthouse. The evidence custodian is out sick, and the office policy states that no evidence can be stored in the locker room if it would exceed 90% capacity. The locker room capacity is defined as the total number of boxes the lockers can hold. You must decide how to store the new boxes without violating policy.
1. Calculate the current total capacity of the locker room and the current number of boxes stored. Determine if the new boxes can be stored without exceeding 90% capacity, and if not, what is the minimum number of boxes that must be removed (by destruction or return) to allow storage of all 8 new boxes.
Read the worked answer
Total capacity = 12 lockers × 5 boxes = 60 boxes. Current boxes: 9 lockers × 5 = 45; 2 lockers × 3 = 6; 1 locker × 0 = 0; total = 51 boxes. 90% capacity = 0.9 × 60 = 54 boxes. With 8 new boxes, total would be 51 + 8 = 59 boxes, which exceeds 54. To store all 8 new boxes, total must be ≤54, so we need to remove at least 59 - 54 = 5 boxes. Removals available: 3 boxes from locker #4 (destruction) and 2 boxes from locker #7 (return) = 5 boxes exactly. Thus, removing all 5 scheduled boxes allows storage of all 8 new boxes (total = 51 - 5 + 8 = 54), exactly at 90% capacity. No additional removal needed.
2. Suppose the destruction of the 3 boxes in locker #4 is delayed and cannot occur this week. What is the minimum number of additional boxes (beyond the 2 from locker #7) that must be removed to store all 8 new boxes? Assume any box can be removed if necessary, but you want to minimize removals.
Read the worked answer
If only the 2 boxes from locker #7 are removed, current boxes become 51 - 2 = 49. Adding 8 gives 57, which exceeds 54 by 3. So we need to remove 3 more boxes. Thus, minimum additional removals = 3 boxes. Total removals would be 2 + 3 = 5 boxes, same as before, but now they must come from other lockers. The key is that the total number of removals required is always 5 to reach 54 boxes with the 8 new ones, regardless of source.