anonymous
  • anonymous
An orchard contains 51 peach trees with each tree yielding an average of 51 peaches. For each 4 additional trees planted, the average yield per tree decreases by 3 peaches. How many trees should be planted to maximize the total yield of the orchard? The number of trees is . (Give your answer as a whole number.)
Mathematics
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anonymous
  • anonymous
An orchard contains 51 peach trees with each tree yielding an average of 51 peaches. For each 4 additional trees planted, the average yield per tree decreases by 3 peaches. How many trees should be planted to maximize the total yield of the orchard? The number of trees is . (Give your answer as a whole number.)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I got my answer 17/.. but they want it as a whole number. any ideas what i might have done wrong?
anonymous
  • anonymous
anonymous
  • anonymous

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anonymous
  • anonymous
anonymous
  • anonymous
17/2*
anonymous
  • anonymous
total peaches = (51 - (3/4) x)*(51+x) where x = # number of additional trees. maximize and if it's not an integer, which ever integer is closest will do the job.
anonymous
  • anonymous
yes i did it exactly like that
anonymous
  • anonymous
and the max occured at 17/2?
anonymous
  • anonymous
then i multiplied them out and to maximize I found the derivative.
anonymous
  • anonymous
well i got f(x)= -3x^2/4+51x/4+2601
anonymous
  • anonymous
and f '(x)= -6x/4+51/4
anonymous
  • anonymous
i set that to zero and got 17/2
anonymous
  • anonymous
so check the yield at x = 8 and x = 9. they're likely the same so either would work. but if you're a farmer, you go with less additional trees to save $
anonymous
  • anonymous
by yield, i mean total yield, not yield per tree.
anonymous
  • anonymous
x = 8 => 2655 peaches x = 9 => 2655 peaches
anonymous
  • anonymous
i tried those also
anonymous
  • anonymous
it says wrong
anonymous
  • anonymous
anonymous
  • anonymous
did you try 8?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
:/
anonymous
  • anonymous
i don't know what to tell you. could it be they want 59 as the asnwer (total number of trees in the orchard)?
anonymous
  • anonymous
woahhhh how is it 59?
anonymous
  • anonymous
its saying correct to that one
anonymous
  • anonymous
did you use the second derivative test? or something?
anonymous
  • anonymous
51 + 8 = 59. there were 51 already planted plus the 8 you added to maximize the total yield.
anonymous
  • anonymous
but if it's 8.5 shouldnt we round it to 9?
anonymous
  • anonymous
so wouldnt it be 60?
anonymous
  • anonymous
question wasn't clear... should have said total number of trees planted in the orchard. you have to think like a farmer. one less tree gives the same yield as one more. what would be better? think of not only the initial cost of the tree but also the watering and care, etc.
anonymous
  • anonymous
ok...
anonymous
  • anonymous
maybe 60 would also work (as an answer) but it's not as practical as 59.
anonymous
  • anonymous
im a little confused on that.
anonymous
  • anonymous
yeah i tried 60 but it kept saying wrong.
anonymous
  • anonymous
i mean mathematically speaking best round is 60 and then adding it to the already planted trees
anonymous
  • anonymous
meaning 51+ 9....
anonymous
  • anonymous
again, you have think like a business person/farmer. think of the problem like this: if you had to cut off fingers to get gold coins in the same scenario, you'd want to cut off as few fingers as possible in order to maximize the number of gold coins. if you got the same number of gold coins for cutting of 8 fingers as you would for cutting off 9 fingers, how many fingers would you cut off?
anonymous
  • anonymous
huh?
anonymous
  • anonymous
how old are you?
anonymous
  • anonymous
this example sounds scary.
anonymous
  • anonymous
yeah, intentionally.
anonymous
  • anonymous
i understand you, but i just don't like the example.lol
anonymous
  • anonymous
thanks anyways, i see the problem clearly now.
anonymous
  • anonymous
lol, sorry. it's just what popped out of my head.
anonymous
  • anonymous
thanks again!
anonymous
  • anonymous
excellent. ask your teacher to be more explicit in what is wanted next time. you're welcome!

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