Cafeteria supplier choice with package excess
A school cafeteria needs to order three items for a week: 240 loaves of bread, 180 litres of milk, and 150 kg of rice. Two suppliers, A and B, quote unit prices but package sizes differ. Supplier A sells bread in 20-loaf crates at $24, milk in 10-litre cartons at $18, and rice in 25-kg sacks at $30. Supplier B sells bread in 30-loaf crates at $33, milk in 6-litre cartons at $12, and rice in 20-kg sacks at $24. Deliveries must be in whole crates, cartons, or sacks, and any excess is usable but has a storage cost of $0.50 per loaf, $0.20 per litre, and $0.40 per kg. Supplier A charges a flat $40 delivery; Supplier B delivers free but requires a minimum order of $500 before delivery. The cafeteria has a storage limit of 300 loaves, 220 litres, and 180 kg. The manager wants the lower total cost including storage and delivery, not simply the lower unit price.
1. For each supplier, calculate the number of whole packages needed for each item, the excess amount, and the package subtotal. Present the results clearly.
Read the worked answer
Supplier A:
- Bread: 240/20=12 crates exactly; cost 12×24=$288; excess 0.
- Milk: 180/10=18 cartons exactly; cost 18×18=$324; excess 0.
- Rice: 150/25=6 sacks exactly; cost 6×30=$180; excess 0. Subtotal=$792.
Supplier B:
- Bread: 240/30=8 crates exactly; cost 8×33=$264; excess 0.
- Milk: 180/6=30 cartons exactly; cost 30×12=$360; excess 0.
- Rice: 150/20=7.5, so 8 sacks; 8×20=160 kg; excess 10 kg; cost 8×24=$192. Subtotal=$816.
2. Include storage and delivery charges, check storage limits, and recommend the lower-cost supplier. Then reassess if the storage limit for rice is reduced to 5 kg.
Read the worked answer
Supplier A: storage $0; delivery $40; total $792+$40=$832. Excess amounts 0,0,0 are within storage limits.
Supplier B: storage=10×0.40=$4; delivery $0 because subtotal $816 exceeds the $500 minimum; total=$816+$4=$820. Excess 10 kg is within the 180 kg rice limit; other excesses are 0. Therefore B is cheaper by $12.
If the rice storage limit becomes 5 kg, B's 10 kg excess is infeasible. B cannot order only 7 sacks because 7×20=140 kg, which is 10 kg short of the 150 kg requirement. A has zero rice excess and remains feasible at $832, so the recommendation switches to A under that tighter limit.