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
plan D

Answer 1

Plan B.

Calculations:
- A: needs $4.00 / $0.10 = 40 weeks.
- D: $4.00 / $0.25 = 16 weeks.
- C: given as 8 weeks.
- B: 8*(1.1)^n ≥ 12 → (1.1)^n ≥ 1.5 → n ≈ ln(1.5)/ln(1.1) ≈ 4.25, so 5 weeks (since after 4 weeks it's still below $12).

Thus Plan B reaches $12 fastest (in 5 weeks).