Expert: Paul Klarreich - 6/24/2008

Question
I have a variation on the peach orchard problem.  What if the average yield per tree is 100 pounds if the peaches are picked now and can be sold for $1.45 per pound now.  However, for every week he waits, the yield increases 5 pounds while the price decreases about $0.06 per pound per week.  After how many weeks should the peaches be picked in order to produce a maximum revenue per tree?

Answer
Questioner:   Rebecca Savell
Category:  Advanced Math
Private:  No
 
Subject:  Calculus
Question:  I have a variation on the peach orchard problem.  What if the average yield per tree is 100 pounds if the peaches are picked now and can be sold for $1.45 per pound now.  However, for every week he waits, the yield increases 5 pounds while the price decreases about $0.06 per pound per week.  After how many weeks should the peaches be picked in order to produce a maximum revenue per tree?
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Hi, Rebecca,

You have to start by selecting a variable, such as:

Let n = number of weeks of waiting.

Then express some things in terms of n:

Yield = 100 + 5n

Price = 145 - 6n

Revenue = Yield * price =  (I think you can handle it from here.)