Alginate Purchasing: Bulk Powder vs. Premeasured Packets
You manage supplies for a dental student clinic that makes 48 alginate impressions per week for 50 weeks each year (2,400 impressions annually). The clinic currently buys alginate in 1 kg bags costing $54.00 each. The manufacturer specifies a 1:2 powder-to-water ratio by weight, and each impression requires 20.0 g of powder mixed with 40.0 g of water. In practice, 10% of the powder in every bag is unusable because of caking at the bottom, and mixing plus spillage wastes another 5% of the powder that is actually used. A sales representative offers premeasured foil packets containing 25 g of powder for $1.60 each. Each packet must be mixed whole with 50 g of water; the unused 5 g of powder cannot be stored for later. The clinic director asks whether switching to packets would be financially justified and how much the bulk price could rise before packets become cheaper.
1. Calculate the annual material cost under the current bulk system and under the packet system, including caking and mixing/spillage losses.
Read the worked answer
Bulk system
- Usable powder per 1 kg bag: 1,000 g × 0.90 = 900 g.
- Powder consumed per impression: 20.0 g × 1.05 = 21.0 g.
- Impressions supported per bag: 900 g ÷ 21.0 g = 42.857.
- Annual bags: 2,400 ÷ 42.857 = 56.0, so exactly 56 bags.
- Annual bulk cost: 56 × $54.00 = $3,024.
Packet system
- One packet is opened per impression because the leftover 5 g cannot be stored.
- Annual packets: 2,400.
- Annual packet cost: 2,400 × $1.60 = $3,840.
The bulk system saves $3,840 − $3,024 = $816 per year, about 21% of the packet cost. The packet's apparent convenience does not offset the 5 g wasted in every packet.
2. At what bulk bag price would the two options cost the same? Express the answer as a price per 1 kg bag and as a percent increase over $54.00.
Read the worked answer
Set the annual bulk cost equal to the annual packet cost:
56 bags × P = $3,840
P = $3,840 ÷ 56 = $68.571…, or about $68.57 per 1 kg bag.
Percent increase over the current $54.00 price:
($68.57 − $54.00) ÷ $54.00 = $14.57 ÷ $54.00 = 0.2698 ≈ 27.0%.
So packets become cheaper only if the bulk bag price rises above about $68.57, a 27% increase. At the current price, bulk remains cheaper even after the 10% caking loss and 5% spillage loss.
3. Next year the clinic expects impression volume to grow by 15%. Recalculate the bulk bags and annual bulk cost, and determine the new break-even bulk price per bag.
Read the worked answer
New annual impressions: 2,400 × 1.15 = 2,760.
Powder required: 2,760 × 21.0 g = 57,960 g.
Bags required: 57,960 g ÷ 900 g per bag = 64.4 bags. Because whole bags must be purchased, round up to 65 bags.
Bulk cost: 65 × $54.00 = $3,510.
Packet cost: 2,760 × $1.60 = $4,416.
New break-even bulk price: $4,416 ÷ 65 = $67.94 per bag.
The break-even price falls slightly from $68.57 to $67.94 because the rounding to 65 bags spreads the packet cost over more bags. Bulk still wins at $54.00.