# Bulk Buy Brain

> Is the bulk pack really cheaper once waste, storage and tied-up cash are counted? Compare a small pack with a bulk pack using how fast you actually use the product, its shelf life, storage cost and the interest your money could earn. The tool computes the effective cost per unit you actually use, your saving or loss, and the largest bulk size worth buying.

Part of usefulweb.site (https://usefulweb.site/). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://bulkbuybrain.usefulweb.site/ (interactive tool at https://bulkbuybrain.usefulweb.site/tool)
- JSON API: POST https://bulkbuybrain.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://bulkbuybrain.usefulweb.site/api/v1/tool)
- OpenAPI: https://bulkbuybrain.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://bulkbuybrain.usefulweb.site/mcp - tool `bulk_buy_brain`

## Inputs
- currency (text): Currency - Shown in results only; no conversion is performed.
- unitLabel (text): Unit
- smallPrice (number, required): Small pack price
- smallQuantity (number, required): Small pack quantity
- bulkPrice (number, required): Bulk pack price
- bulkQuantity (number, required): Bulk pack quantity
- consumptionPerWeek (number, required): You use per week
- shelfLifeWeeks (number): Shelf life once bought - Leave empty for non-perishables.
- storageCostPerWeek (number): Storage cost of the bulk pack - Optional: freezer energy, rented space…
- interestRatePercent (number): Interest your cash could earn

## Method
- Small-pack unit price ps = small price ÷ small quantity (small packs bought as needed, no waste). Bulk unit price pb = bulk price ÷ bulk quantity.
- Usable quantity = min(bulk quantity, consumption per week × shelf life); waste = bulk quantity − usable quantity.
- Weeks held = usable quantity ÷ consumption per week. Storage cost = storage cost per week × weeks held.
- Opportunity cost = bulk price × interest rate × (weeks held ÷ 52.18) ÷ 2 (the prepaid amount is drawn down linearly, so on average half is tied up).
- Effective cost per used unit = (bulk price + storage + opportunity cost) ÷ usable quantity. Savings = ps × usable quantity − bulk total cost.
- Max worthwhile size: the largest Q for which pb·Q + storage + opportunity cost ≤ ps × usable(Q), solved in closed form for the no-waste and the waste regime.