Maize meal: the label price is not the real price
A school feeding committee must buy at least 200 kg of usable maize meal for the month; grain lost to spillage and moisture does not count. Three suppliers quote: Supplier P sells 12.5 kg paper bags at P101.25 each, but paper bags lose about 4% of their contents. Supplier Q sells 10 kg plastic bags at P82.00 each, with about 1% loss. Supplier R sells 25 kg sacks at P198.00 each, with about 6% loss because the sacks are stored on a damp floor. Bags cannot be split, and the committee's budget is P1 750. Last month the committee bought whichever supplier had the lowest price per kilogram on the label and ran short of meal by the third week. The chairperson wants a written recommendation this time.
1. Compare the true cost per **usable** kilogram of Suppliers P, Q and R. Does the cheapest label price give the cheapest meal?
Read the worked answer
Work out the label price per kilogram, then divide by the fraction that survives storage.
- P: 101.25 ÷ 12.5 = P8.10 per kg bought. Only 96% is usable, so cost per usable kg = 8.10 ÷ 0.96 = P8.4375.
- Q: 82.00 ÷ 10 = P8.20 per kg bought. 8.20 ÷ 0.99 = P8.2828 per usable kg.
- R: 198.00 ÷ 25 = P7.92 per kg bought. 7.92 ÷ 0.94 = P8.4255 per usable kg.
The label ranking is P (8.10) < Q (8.20) < R (7.92 is actually lowest, so the true label ranking is R < P < Q). After loss the ranking is Q (8.28) < R (8.43) < P (8.44). So the answer is no: P looks cheapest on the shelf but is the most expensive per usable kilogram, because it loses four times as much as Q. A loss percentage is a multiplier, not a small detail - it must be applied before any price comparison.
2. Using whole bags only, find the cheapest purchase from each supplier that yields at least 200 kg of usable meal, and state which suppliers fit the P1 750 budget.
Read the worked answer
Gross kilograms needed = 200 ÷ (fraction usable), then round up to whole bags.
- P: 200 ÷ 0.96 = 208.33 kg needed; 208.33 ÷ 12.5 = 16.67 → 17 bags. Gross 17 × 12.5 = 212.5 kg; usable 212.5 × 0.96 = 204.0 kg. Cost 17 × 101.25 = P1 721.25.
- Q: 200 ÷ 0.99 = 202.02 kg needed; 202.02 ÷ 10 = 20.2 → 21 bags. Gross 210 kg; usable 210 × 0.99 = 207.9 kg. Cost 21 × 82 = P1 722.00.
- R: 200 ÷ 0.94 = 212.77 kg needed; 212.77 ÷ 25 = 8.51 → 9 bags. Gross 225 kg; usable 225 × 0.94 = 211.5 kg. Cost 9 × 198 = P1 782.00.
P and Q both fit the budget; R exceeds it by P32 and is eliminated even though its per-usable-kg cost is good, because 9 sacks force a large over-buy. Rounding up to whole bags scrambles the per-kilogram ranking: P is the cheapest in cash by 75 thebe even though Q is cheaper per usable kilogram, since P's 12.5 kg bag happens to fit 200 kg with less waste.
3. The committee wants one recommendation. Decide, justify it with your figures, and list what should be checked before the order is placed.
Read the worked answer
Decision: buy 21 bags of Supplier Q.
Why: the cash difference is P1 722.00 − P1 721.25 = P0.75, under 0.05% of the budget - far too small to be a real reason. What separates them is what the money buys: Q delivers 207.9 usable kg against P's 204.0 kg, i.e. 3.9 kg more food for 75 thebe (about P0.19 per extra kilogram), and Q is cheaper per usable kilogram (P8.28 vs P8.44). P is only cheaper in headline cash. R is rejected because P1 782.00 breaks the P1 750 budget.
Check before ordering:
- The 4% and 1% loss figures are estimates, not measurements. If P's bags were stored in a sealed dry bin and its loss fell to 1%, P's cost would fall to P8.18 per usable kg and it would win - so the recommendation is only as good as the loss data.
- Storage space for 210 kg and protection from damp (the very problem that damaged R's sacks).
- Delivery cost and delay, which are not in the quotes.
- Whether any over-buy beyond 200 kg can be used before it spoils; if not, the 7.9 kg surplus has no value and the comparison changes.