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.)

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- anonymous

I got my answer 17/.. but they want it as a whole number. any ideas what i might have done wrong?

- anonymous

- anonymous

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## More answers

- anonymous

- anonymous

17/2*

- 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

yes i did it exactly like that

- anonymous

and the max occured at 17/2?

- anonymous

then i multiplied them out and to maximize I found the derivative.

- anonymous

well i got f(x)= -3x^2/4+51x/4+2601

- anonymous

and f '(x)= -6x/4+51/4

- anonymous

i set that to zero and got 17/2

- 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

by yield, i mean total yield, not yield per tree.

- anonymous

x = 8 => 2655 peaches
x = 9 => 2655 peaches

- anonymous

i tried those also

- anonymous

it says wrong

- anonymous

##### 1 Attachment

- anonymous

did you try 8?

- anonymous

yeah

- 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

woahhhh how is it 59?

- anonymous

its saying correct to that one

- anonymous

did you use the second derivative test? or something?

- anonymous

51 + 8 = 59. there were 51 already planted plus the 8 you added to maximize the total yield.

- anonymous

but if it's 8.5 shouldnt we round it to 9?

- anonymous

so wouldnt it be 60?

- 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

ok...

- anonymous

maybe 60 would also work (as an answer) but it's not as practical as 59.

- anonymous

im a little confused on that.

- anonymous

yeah i tried 60 but it kept saying wrong.

- anonymous

i mean mathematically speaking best round is 60 and then adding it to the already planted trees

- anonymous

meaning 51+ 9....

- 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

huh?

- anonymous

how old are you?

- anonymous

this example sounds scary.

- anonymous

yeah, intentionally.

- anonymous

i understand you, but i just don't like the example.lol

- anonymous

thanks anyways, i see the problem clearly now.

- anonymous

lol, sorry. it's just what popped out of my head.

- anonymous

thanks again!

- anonymous

excellent. ask your teacher to be more explicit in what is wanted next time.
you're welcome!

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