Question

Niveen makes muffins and sells them for $0.65 each. To make 12 muffins, she must spend $5.25 on muffin mix, $0.75 on vegetable oil, and $0.87 on eggs. The smallest batch of muffins Niveen can make is 12 muffins.



Which of the following situations would result in Niveen earning a profit?


selling 30 muffins at the original price


selling 36 muffins at a discount rate of 10% off the original price


selling 39 muffins while using half as many eggs per batch


selling 48 muffins and using $1.85 worth of butter per batch instead of vegetable oil

Answer 1

First compute the base cost per 12‑muffin batch:
mix $5.25 + oil $0.75 + eggs $0.87 = $6.87 per batch.
Price per muffin = $0.65.

1) Sell 30 muffins. Must make 3 batches = 36 muffins.
Cost = 3 × $6.87 = $20.61. Revenue = 30 × $0.65 = $19.50 → loss $1.11.

2) Sell 36 muffins at 10% off. 36 muffins = 3 batches.
Discounted price = $0.65 × 0.9 = $0.585. Revenue = 36 × $0.585 = $21.06.
Cost = 3 × $6.87 = $20.61 → profit $0.45. (Profit)

3) Sell 39 muffins using half the eggs per batch. Must make 4 batches (48 muffins).
New egg cost per batch = $0.87/2 = $0.435. New batch cost = $5.25 + $0.75 + $0.435 = $6.435.
Total cost = 4 × $6.435 = $25.74. Revenue = 39 × $0.65 = $25.35 → loss $0.39.

4) Sell 48 muffins using $1.85 butter instead of oil. 48 = 4 batches.
New batch cost = $5.25 + $1.85 + $0.87 = $7.97. Total cost = 4 × $7.97 = $31.88.
Revenue = 48 × $0.65 = $31.20 → loss $0.68.

Only the second situation (selling 36 muffins at 10% off) yields a profit.