Shelving Before the Inspection
The registry of a municipal court must shelve 1,470 case files before an inspection. Shelves come in units: each unit has 6 shelves and each shelf holds exactly 28 files. Ninety-six of the files are oversized ledger binders, and the office rule is that each oversized item occupies the space of two ordinary files. Eight units are already in the room, all empty. The supplier delivers extra units at $215 each, and the office has $500 left in its furniture budget for the quarter. The clerk in charge proposes to order three units 'to be safe' and to shelve the oversized binders last so that they can be 'squeezed in' at the end.
1. How many shelving units does the job actually require, and how many must be ordered beyond the eight already present?
Read the worked answer
Convert everything to one unit of measure - ordinary-file slots.
- Ordinary files: 1,470 − 96 = 1,374
- Oversized files in slots: 96 × 2 = 192
- Total demand: 1,374 + 192 = 1,566 slots
Capacity per unit: 6 shelves × 28 files = 168 slots
Units needed: 1,566 ÷ 168 = 9.32… → round up, because a partly filled tenth unit is still a unit that must be bought. Total = 10 units.
Order: 10 − 8 = 2 additional units.
Rounding down to 9 would leave 1,512 slots for 1,566 slots of material - a shortfall of 54 slots, about two shelves.
2. Evaluate the clerk's two proposals - ordering three units, and shelving the oversized binders last - against the numbers and the budget.
Read the worked answer
Three units: 3 × $215 = $645, against $500 available. That overspends by $145 and leaves no contingency for freight or damage. Two units cost 2 × $215 = $430, leaving $70, and deliver exactly the 10 units the arithmetic requires. So three is not 'safe', it is unaffordable; two is both sufficient and within budget.
'Shelve the oversized binders last': this is a scheduling fix applied to a space problem, and space does not defer. Once 1,344 slots are filled, the room is full. Leaving the non-standard items to the end means the shortfall surfaces at the worst moment - when the room is already crowded and the inspection is near - and it invites the person doing the shelving to override the double-space rule to 'make it fit', which corrupts the shelf count for the next inventory.
Correct handling: order two units, declare the 168-slot capacity of each shelf, and shelve oversized items as they arise so the running count on the shelf list reflects the rule.
3. The inspection is moved to tomorrow and only the eight units on hand can be used. What is the shortfall in slots, and what is the smallest number of ordinary files that must be moved out if the oversized binders are not moved?
Read the worked answer
Capacity on hand: 8 units × 168 slots = 1,344 slots
Demand: 1,566 slots
Shortfall: 1,566 − 1,344 = 222 slots
If the binders stay: they consume 192 slots, leaving 1,344 − 192 = 1,152 slots for ordinary files. Ordinary files total 1,374, so 1,374 − 1,152 = 222 ordinary files must go elsewhere.
The two figures agree, which is the check that the reasoning is sound: a slot shortfall of 222 is met by removing 222 ordinary files, since every ordinary file occupies exactly one slot. Note the tempting error of moving 222 files at random - moving any oversized binder frees two slots but counts as one file, so the removal count and the slot count diverge unless the clerk tracks them separately.