Question

Hi if anyone can solve this I woul be really grateful nobody in my calculus help could solve it :
An orchard contains 50 peach trees with each tree yielding an average of 52 peaches. For each 2 additional trees planted, the average yield per tree decreases by 12 peaches. How many trees should be planted to maximize the total yield of the orchard?

Answer 1

please break down with steps

Answer 2

Every 2 trees added decreases the yield of ALL the other trees by 12?

Answer 3

That's how the question is worded but I am not sure there are similar problems online but again I am not sure

Answer 4

because is adding 2 trees decreases the yield of ALL trees, then adding 2 trees would decrease total yield from 2600 with 50 trees to 2080 with 52 trees, meaning the tree farm is already optimized.

Answer 5

because if*

Answer 6

wait how did you get those numbers 2600 and 2080

Answer 7

and also I put 50 and that was wrong

Answer 8

if you have 50 trees yielding an average of 52 peaches per tree, the average yield is simply 50*52=2600, and if adding 2 trees (50+2)=52 decreases each trees yield by 12, (52-12)=40 then total yield is (52trees*40)=2080. Im a little confused because this isnt really a calculus problem as is

Answer 9

its more than 50? because then it would potentially be more complicated.

Answer 10

again not sure I thought it would be a derivative problem like this : click the link : http://answers.yahoo.com/question/index?qid=20070410084113AArS3CW

Answer 11

its #2 on the link

Answer 12

I am so confused

Answer 13

decreases by 12 peaches or 12%? I think it would make more sense if %

Answer 14

For each 2 additional trees planted, the average yield per tree decreases by 12 peaches

maybe they mean

For each 2 additional trees planted, the average yield per *additional* tree decreases by 12 peaches

Answer 15

if it were 12% then it would be
y=(52-0.12x)(50+x) which is a downward facing parabola with maximum at (575/3) or 191.6666 trees which you would round to 192 trees. This would make more sense

Answer 16

192 is not being accepted....

Answer 17

I am looking at so many versions of this problem and doing step by steps and wrong wrong wrong

Answer 18

anyone give a shot?? another perspective pleaseee :(