Forno Nero: Is a 10% Price Cut Worth It?
Forno Nero is a 40-seat bakery near a university campus. Each morning it bakes focaccia slices and biscotti for the lunch rush. Daily fixed costs are €540. A focaccia slice sells for €4.50 and costs €1.80 in ingredients and packaging; a biscotti sells for €1.20 and costs €0.45. The single oven can handle at most 900 'focaccia-equivalent' units per day, where one biscotti counts as 0.6 of a focaccia because it occupies less space. Yesterday the shop sold 600 focaccia slices and 400 biscotti, which used 840 oven-equivalent units. The owner is considering cutting the focaccia price by 10%, to €4.05, expecting focaccia volume to rise by 25% while biscotti demand stays at 400; the oven limit would then bind. The owner's rule is that any change must leave daily profit at least as high as it is now.
1. Compute the current daily profit and the break-even number of focaccia slices, holding biscotti sales at 400 per day.
Read the worked answer
Unit contribution margins
- Focaccia: €4.50 − €1.80 = €2.70
- Biscotti: €1.20 − €0.45 = €0.75
Current profit
- Focaccia: 600 × 2.70 = €1,620
- Biscotti: 400 × 0.75 = €300
- Total contribution = €1,920; minus fixed costs €540 → €1,380 per day.
Break-even with biscotti fixed at 400
- Biscotti already contribute €300, so focaccia must cover 540 − 300 = €240.
- 240 ÷ 2.70 = 88.9, so 89 slices are needed (88 would leave a small shortfall).
At 89 slices the oven load is 89 + 0.6×400 = 329 units, far below capacity, so the break-even point is demand-feasible.
2. Is the proposed price cut feasible at the assumed volumes? If not, find the profit-maximising feasible plan and decide whether to adopt the cut.
Read the worked answer
Feasibility check
- New focaccia volume: 600 × 1.25 = 750 slices.
- Oven load: 750 + 0.6×400 = 750 + 240 = 990 units, which exceeds the 900-unit limit by 90 units. The plan as stated cannot be run.
Which product should give way? Compare contribution per oven-equivalent unit:
- Focaccia at the new price: (4.05 − 1.80) = €2.25 per unit, and 1 oven unit each → €2.25 per oven unit.
- Biscotti: 0.75 ÷ 0.6 = €1.25 per oven unit.
Focaccia still earns more per oven unit, so keep focaccia at its demand ceiling of 750 and fill the remaining 150 oven units with biscotti: 150 ÷ 0.6 = 250 biscotti.
Profit of the best feasible plan
- 750 × 2.25 = €1,687.50
- 250 × 0.75 = €187.50
- Contribution €1,875 − €540 = €1,335
This is €45 below the current €1,380, so the cut should be rejected under the owner's rule.
3. What focaccia volume increase would the 10% cut need in order to hold profit at €1,380, and can the oven accommodate it?
Read the worked answer
Required volume if biscotti stay at 400 Target contribution = profit + fixed costs = 1,380 + 540 = €1,920. Biscotti contribute €300, so focaccia must contribute €1,620. 1,620 ÷ 2.25 = 720 slices, i.e. a 20% increase over 600.
Capacity check
- Oven load: 720 + 0.6×400 = 720 + 240 = 960 units > 900. Infeasible.
- The most focaccia possible while keeping 400 biscotti is 900 − 240 = 660 slices, giving profit 660 × 2.25 + 300 − 540 = €1,245.
Reallocating oven space toward focaccia helps but is not enough: the best plan found in the previous task yields €1,335. No feasible plan at the lower price reaches €1,380, so the cut fails even before demand uncertainty is considered.