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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.)
 5 months ago
 5 months ago
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.)
 5 months ago
 5 months ago

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mathcalculusBest ResponseYou've already chosen the best response.0
I got my answer 17/.. but they want it as a whole number. any ideas what i might have done wrong?
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
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.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
yes i did it exactly like that
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
and the max occured at 17/2?
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
then i multiplied them out and to maximize I found the derivative.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
well i got f(x)= 3x^2/4+51x/4+2601
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
and f '(x)= 6x/4+51/4
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i set that to zero and got 17/2
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
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 $
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
by yield, i mean total yield, not yield per tree.
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
x = 8 => 2655 peaches x = 9 => 2655 peaches
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i tried those also
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
i don't know what to tell you. could it be they want 59 as the asnwer (total number of trees in the orchard)?
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
woahhhh how is it 59?
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
its saying correct to that one
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
did you use the second derivative test? or something?
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
51 + 8 = 59. there were 51 already planted plus the 8 you added to maximize the total yield.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
but if it's 8.5 shouldnt we round it to 9?
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
so wouldnt it be 60?
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
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.
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
maybe 60 would also work (as an answer) but it's not as practical as 59.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
im a little confused on that.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
yeah i tried 60 but it kept saying wrong.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i mean mathematically speaking best round is 60 and then adding it to the already planted trees
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
meaning 51+ 9....
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
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?
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
this example sounds scary.
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
yeah, intentionally.
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i understand you, but i just don't like the example.lol
 5 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
thanks anyways, i see the problem clearly now.
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
lol, sorry. it's just what popped out of my head.
 5 months ago

pgpilot326Best ResponseYou've already chosen the best response.0
excellent. ask your teacher to be more explicit in what is wanted next time. you're welcome!
 5 months ago
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