Comparing Unit Prices Across Package Sizes
A café compares three package sizes of the same coffee beans. Size A: 12 oz for $9.60. Size B: 18 oz for $13.50. Size C: 30 oz for $21.00. The café uses about 2.5 oz of beans per day and operates 6 days a week, so it needs roughly 15 oz per week. The owner wants the lowest cost per ounce, but also wants to avoid beans going stale: an open package should be used within about 3 weeks. A supplier claims Size C is always cheapest per ounce because it is the largest; the owner wants that claim tested and a recommendation that respects both price and the 3-week freshness limit.
1. Compute the unit price (cost per ounce) for each size and rank them.
Read the worked answer
A: 9.60 ÷ 12 = $0.80 per oz. B: 13.50 ÷ 18 = $0.75 per oz. C: 21.00 ÷ 30 = $0.70 per oz.
Ranking (cheapest first): C ($0.70) < B ($0.75) < A ($0.80).
Check: 18 × 0.75 = 13.50 ✓; 30 × 0.70 = 21.00 ✓; 12 × 0.80 = 9.60 ✓. The supplier's claim holds here - C is indeed cheapest per ounce.
2. Given ~15 oz/week usage and a 3-week freshness window, how many ounces can the café use before an open package goes stale, and does Size C fit that window?
Read the worked answer
Usable before stale: 15 oz/week × 3 weeks = 45 oz.
Size C is 30 oz, which is less than 45 oz, so a single 30-oz package would be fully used in 30 ÷ 15 = 2 weeks - within the 3-week window. So C fits.
Size B (18 oz) lasts 18 ÷ 15 = 1.2 weeks; Size A lasts 12 ÷ 15 = 0.8 weeks. Both also fit.
So the freshness limit does not rule out C; all three are consumable within 3 weeks. The lowest unit price (C) is therefore also defensible on freshness grounds.
3. If the café instead used only 8 oz per week, would Size C still be advisable under the 3-week limit? Recompute and recommend.
Read the worked answer
At 8 oz/week, usable before stale = 8 × 3 = 24 oz.
Size C is 30 oz > 24 oz, so ~6 oz would go stale before it is used - C no longer fits the freshness window. Size B is 18 oz ≤ 24 oz (lasts 18 ÷ 8 = 2.25 weeks) - fits. Size A is 12 oz ≤ 24 oz (lasts 1.5 weeks) - fits.
Among fitting sizes, B ($0.75/oz) beats A ($0.80/oz). Recommendation: buy Size B. This shows the supplier's "largest is always cheapest" claim is only about unit price, not about total cost once waste from staleness is counted - the cheapest-per-ounce size can be the worst choice when usage is low.