Question

Felix’s Feed Mill sells chicken feed for $8.00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans.

Plan A: Raise the price by $0.10 each week until the price reaches $12.00.

Plan B: Raise the price by 10 percent each week until the price reaches $12.00.

Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.00.

Plan D: Raise the price by $0.25 each week until the price reaches $12.00.

Which plan will result in the price of the feed reaching $12.00 fastest?
plan A
plan B
plan C

Answer 1

Plan B.

Quick comparison:
- A: $0.10/week → (12−8)/0.10 = 40 weeks.
- B: 10%/week → need n with 8(1.1^n) ≥ 12. n = ln(1.5)/ln(1.1) ≈ 4.25, so after 5 weekly increases the price exceeds $12 (8·1.1^5 ≈ $12.88).
- C: by design reaches $12 in 8 weeks.
- D: $0.25/week → (12−8)/0.25 = 16 weeks.

Thus plan B reaches $12 fastest.