# There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, theoutput per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the totaloutput of trees ?

bharat bajaj IIT Delhi
9 years ago
The output for x no. of trees is then : (800 - 10n)(50+n)
Hence, O = 300n - 10n^2 + 40000
Differentiate it :
300 - 20n = 0
hence, n = 15
Hence, 15 trees should be added.
Thanks
Bharat Bajaj
IIT Delhi
sidduchinnu
37 Points
9 years ago
x no. of trees is then : (800 - 10n)(50+n) = 300n - 10n^2 + 4000 differentiate it : 300 - 20n = 0 n = 15 there fore, 15 trees should be added.
8 years ago
let number of additional tree is n , now total trees =50+n
apple production per tree =800-10n
total production =(50+n)(800-10n)
= -(10n^2-300n-40000)
f'(n)= 20n-300=0
n=15
b.tech, iit delhi

`let number of additional tree is n , now total trees =50+napple production per tree =800-10ntotal production =(50+n)(800-10n)= -(10n^2-300n-40000)f'(n)= 20n-300=0n=15sher mohammadb.tech, iit delhi`
$A_{n}=(50+n)(800-10n)\,\,\,\,\,\,where\,n\,no.\,of\,extra\,tree\,planted\\ =>\frac{\mathrm{d} A_{n}}{\mathrm{d} n}=800-10n-10(50+n)\\ =>n=15\\$