The Discounted Bulk Order
A school office orders printer paper. The supplier offers: single reams at $6.50 each; a box of 5 reams at $30.00; or a pallet of 40 reams at $220.00. The office needs 46 reams for the term and has a storage limit of 50 reams. Delivery is free above $200 and costs $15 below that. The office currently holds 4 reams in stock. A staff member proposes buying one pallet plus one box, arguing 'bulk is always cheaper'. The budget officer warns that unused paper at term end is wasted, and last term 9 reams were left over.
1. Calculate the cost of the staff member's proposal and check it against the requirement.
Read the worked answer
One pallet (40) plus one box (5) gives 45 reams. With 4 already in stock, total available is 49, which covers the 46 needed but leaves 3 spare - within the 50 storage limit. Cost is $220 + $30 = $250, above $200, so delivery is free. Total $250. The proposal is feasible but note it buys 45 reams when only 42 are needed (46 minus 4 in stock), so 3 reams are surplus.
2. Is there a cheaper feasible option? Show the comparison.
Read the worked answer
Needed from supplier: 46 − 4 = 42 reams. Option A: pallet (40) + box (5) = 45 reams, $250. Option B: eight boxes = 40 reams, plus 2 single reams = $240 + $13 = $253, but only 42 reams exactly - $253, more than A. Option C: pallet (40) + 2 singles = $220 + $13 = $233, giving 42 reams exactly. That is below $200? No - $233 exceeds $200, so delivery is free. Total $233, and no surplus. Option C is cheapest and waste-free. The reasoning tests whether 'bulk is always cheaper' survives an exact-need calculation.