Hāngi fundraiser: when a committed meat order changes the break-even
Hine chairs the whānau committee at Te Horo marae. The group needs $1,500 for transport to a regional kapa haka festival, and the plan is a hāngi fundraiser selling packs at $18 each to 140 presold customers.
The committee has already committed to buying one 45 kg lot of meat at $11.80 per kilogram - the supplier will not split the order. Everything else scales with the number of packs: $2.15 of vegetables and $0.75 of packaging per pack. Gas, wood and hāngi gear hire come to a fixed $340 whatever the number of packs is made.
Three days out, only 118 customers have paid. The meat order cannot be changed, but the committee can still buy vegetables and packaging to match whatever number of packs it actually makes. Hine needs to know whether $18 still works, and if not, what price to charge, before the notices go out on the marae Facebook page.
1. Calculate the profit if 118 packs are sold at $18 each, and state whether the $1,500 target is met. Show each cost line.
Read the worked answer
Fixed costs (do not change with volume)
- Meat: 45 kg × $11.80 = $531.00 - already committed, so it stays at $531 even though 22 customers dropped out.
- Gas, wood, gear hire: $340.00
Costs that scale with volume
- Vegetables: $2.15 + packaging $0.75 = $2.90 per pack
- 118 packs × $2.90 = $342.20
Totals
- Cost = $531.00 + $340.00 + $342.20 = $1,213.20
- Revenue = 118 × $18 = $2,124.00
- Profit = $2,124.00 − $1,213.20 = $910.80
The target is missed by $1,500 − $910.80 = $589.20.
Note the trap: a candidate who divides the meat cost by 140 and re-multiplies by 118 gets a smaller cost and a profit that is too high. The meat is a sunk lump-sum purchase, so the cost per pack rises as the number of packs falls ($1,213.20 ÷ 118 = $10.28 per pack, not $6.69).
2. What price per pack, to the nearest 10 cents, would deliver exactly the $1,500 profit if only 118 packs are made? Check your answer.
Read the worked answer
Work backwards from the target rather than guessing and testing.
Required revenue = target profit + total cost = $1,500 + $1,213.20 = $2,713.20
Price = $2,713.20 ÷ 118 = $22.9932…
To the nearest 10 cents: $23.00 per pack.
Check: 118 × $23.00 = $2,714.00; $2,714.00 − $1,213.20 = $1,500.80. That clears the target by 80 cents.
Rounding down to $22.90 would give 118 × $22.90 = $2,702.20, a profit of $1,489.00 - $11 short. When a target must be met, always round prices up, not to nearest.
Judgement to state: $23.00 is a 28% price rise on $18, announced three days out, which risks further cancellations. The committee should compare this against the option in the next task before deciding.
3. A committee member suggests keeping the price at $18 and simply selling more packs. The 45 kg of meat covers a maximum of 140 packs. Test whether that plan reaches $1,500, and find the lowest whole-dollar-friendly price that does.
Read the worked answer
Selling out at $18
- Cost = $531.00 (meat) + $340.00 (fixed) + (140 × $2.90 = $406.00) = $1,277.00
- Revenue = 140 × $18 = $2,520.00
- Profit = $2,520.00 − $1,277.00 = $1,243.00
Still $257 short of $1,500. Selling more packs alone cannot fix this because the meat caps output at 140 - the extra 22 sales only add $18 − $2.90 = $15.10 of contribution each.
Minimum price at full sell-out Required revenue = $1,500 + $1,277.00 = $2,777.00 Price = $2,777.00 ÷ 140 = $19.836… → $19.90 (check: 140 × $19.90 = $2,786.00, profit $1,509.00).
Judgement: $19.90 only works if all 140 packs sell. Given that 22 of 140 presold customers already withdrew, that is optimistic. $23.00 at 118 packs is the safer plan; $19.90 at 140 is the better-value plan for the community but carries the risk of falling short. Either way the committee must decide before printing prices, and should say which assumption it is relying on.