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?

Question

Nikolai Harper

Mathematics

9 May, 13:43

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?

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Answers (1)

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Arias · Answer 1

Hi!

First of all plan A is definitely slower than plan D on reaching $12.00. Plan C takes 8 weeks to do so. So, how many weeks does it take to reach $12.00 with plans B and C?

Let n be that number.

With plan D : 8+0.25n = 12 so n = 16 : that is slower than plan C.

Now let's consider plan B:

8*1.1^n = 12, so : ln (8) + n*ln (1.1) = ln (12), therefore

n = (ln (12) - ln (8)) / ln (1.1) ≈ 4.3 weeks.

So plan B will result in the price of the feed reaching $12.00 fastest.