Question

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.)

Answer 1

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

Answer 2

@agent0smith

Answer 3

@pgpilot326

Answer 4

@zepdrix

Answer 5

17/2*

Answer 6

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.

Answer 7

yes i did it exactly like that

Answer 8

and the max occured at 17/2?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

i set that to zero and got 17/2

Answer 13

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 $

Answer 14

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

Answer 15

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

Answer 16

i tried those also

Answer 17

it says wrong

Answer 18

did you try 8?

Answer 19

yeah

Answer 20

:/

Answer 21

i don't know what to tell you. could it be they want 59 as the asnwer (total number of trees in the orchard)?

Answer 22

woahhhh how is it 59?

Answer 23

its saying correct to that one

Answer 24

did you use the second derivative test? or something?

Answer 25

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

Answer 26

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

Answer 27

so wouldnt it be 60?

Answer 28

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.

Answer 29

ok...

Answer 30

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

Answer 31

im a little confused on that.

Answer 32

yeah i tried 60 but it kept saying wrong.

Answer 33

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

Answer 34

meaning 51+ 9....

Answer 35

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?

Answer 36

huh?

Answer 37

how old are you?

Answer 38

this example sounds scary.

Answer 39

yeah, intentionally.

Answer 40

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

Answer 41

thanks anyways, i see the problem clearly now.

Answer 42

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

Answer 43

thanks again!

Answer 44

excellent. ask your teacher to be more explicit in what is wanted next time.

you're welcome!