Calculus 1: Max-Min Problems (14 of 30) Maximizing Apple Orchard Production

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In this video I will find the number of tree=? that will maximize the yield of apples.

Next video in this series can be seen at:
  1. Michel van Biezen
  2. ilectureonline
  3. ilectureonline.com
  4. Mike
  5. Mike van Biezen
  6. van Biezen
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I would be stupid to add 6 more trees and a lot of work (pruning & training) for so little apples.
21% more trees = 3% more yield.

HelloPiya
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Hi Michel, Many thanks for your videos. Another great video. I believe at 3: 44 11600-280x-10x square. Thank you

zeesamuel
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I used a different relationship but got the exact same answer. Wondering if I just got lucky. Here's my reasoning....

yield per acre, ya, equals the product of the number of trees (n) and the yield per tree.

The yield per tree (yt) is a function of the number of trees per acre such that when there are 28 trees per acre the yield per tree is 400 kg. yt = 400 - 10(n - 28) where n is the number of trees per acre.

thus, ya = n * yt = n*(680 - 10n) = 680n - 10n^2

from there just follow the usual strategy and you get n = 34 which by the equation for ya above yields 11560 kg/acre.

Seem reasonable?

This is a great set of problems, BTW. Really enjoying going through them!

pipertripp
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There is a small typo at 3:32. It should be 400x. (This is said correctly but not written.)
Great video overall.

tpthpt