The Split Bill
A food truck sells two lunch packages. The Standard box costs the truck $4.20 in ingredients and sells for $9.00. The Deluxe box costs $6.80 and sells for $13.50. On a typical day the truck sells 150 boxes total, and 60 of them are Deluxe.
Daily fixed costs - fuel, permits, insurance, and the owner's time - total $520. The truck has capacity for 220 boxes per day.
The owner is considering a promotion: cut the Deluxe price to $12.00. She estimates this would raise Deluxe sales to 90 boxes per day and leave Standard sales unchanged at 90. She also expects total volume to stay at 150 because of staffing limits at the window.
1. Calculate the truck's current daily profit, then calculate the profit under the proposed promotion. Show your work.
Read the worked answer
Current day
- Standard: 90 boxes × ($9.00 − $4.20) = 90 × $4.80 = $432.00
- Deluxe: 60 boxes × ($13.50 − $6.80) = 60 × $6.70 = $402.00
- Total contribution: $834.00
- Subtract fixed costs: $834.00 − $520.00 = $314.00 profit
Under the promotion
- Standard: 90 × $4.80 = $432.00 (unchanged)
- Deluxe margin falls to $12.00 − $6.80 = $5.20
- Deluxe: 90 × $5.20 = $468.00
- Total contribution: $900.00
- Subtract fixed costs: $900.00 − $520.00 = $380.00 profit
The promotion raises daily profit by $66.00, or about 21%.
2. The owner worries that the promotion "gives away $1.50 on every Deluxe box." Address that concern using the numbers, and state one condition under which the promotion would fail.
Read the worked answer
The $1.50 concern is real but incomplete. Cutting the price does lose $1.50 per Deluxe box, but it also sells 30 more of them. The question is whether the extra volume outweighs the lower margin.
- Lost margin on the 60 boxes that would have sold anyway: 60 × $1.50 = $90.00 lost.
- Gain from the 30 additional boxes: 30 × $5.20 = $156.00 gained.
- Net effect: +$66.00 per day, matching the profit comparison.
So the promotion works because the added volume more than covers the discount. The break-even point is the extra boxes needed to recover the $90: $90 ÷ $5.20 ≈ 17.3, so about 18 additional Deluxe boxes. The owner expects 30, comfortably above that.
When it would fail: if the extra Deluxe sales came from customers who would otherwise have bought Standard boxes. A Standard box earns $4.80; a discounted Deluxe earns $5.20, so the loss is small per swap - but if many Standard buyers traded up, the gain would shrink fast. If all 30 new Deluxe buyers had been Standard buyers, the gain would be only 30 × ($5.20 − $4.80) = $12.00, and any drop in total volume would erase it. The promotion also fails if it cannot actually draw new customers, or if the kitchen cannot keep up at higher Deluxe volume.