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mathcalculus
Group Title
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.)
 one year ago
 one year ago
mathcalculus Group Title
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.)
 one year ago
 one year ago

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mathcalculus Group TitleBest 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?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@agent0smith
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@pgpilot326
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@zepdrix
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
17/2*
 one year ago

pgpilot326 Group TitleBest 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.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
yes i did it exactly like that
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
and the max occured at 17/2?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
then i multiplied them out and to maximize I found the derivative.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
well i got f(x)= 3x^2/4+51x/4+2601
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
and f '(x)= 6x/4+51/4
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i set that to zero and got 17/2
 one year ago

pgpilot326 Group TitleBest 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 $
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
by yield, i mean total yield, not yield per tree.
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
x = 8 => 2655 peaches x = 9 => 2655 peaches
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i tried those also
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
it says wrong
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
did you try 8?
 one year ago

pgpilot326 Group TitleBest 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)?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
woahhhh how is it 59?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
its saying correct to that one
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
did you use the second derivative test? or something?
 one year ago

pgpilot326 Group TitleBest 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.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
but if it's 8.5 shouldnt we round it to 9?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so wouldnt it be 60?
 one year ago

pgpilot326 Group TitleBest 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.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
ok...
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
maybe 60 would also work (as an answer) but it's not as practical as 59.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
im a little confused on that.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
yeah i tried 60 but it kept saying wrong.
 one year ago

mathcalculus Group TitleBest 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
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
meaning 51+ 9....
 one year ago

pgpilot326 Group TitleBest 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?
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
how old are you?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
this example sounds scary.
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
yeah, intentionally.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i understand you, but i just don't like the example.lol
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
thanks anyways, i see the problem clearly now.
 one year ago

pgpilot326 Group TitleBest ResponseYou've already chosen the best response.0
lol, sorry. it's just what popped out of my head.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
thanks again!
 one year ago

pgpilot326 Group TitleBest 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!
 one year ago
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