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

The output for x no. of trees is then : (800 - 10n)(50+n)

Approved

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.

let number of additional tree is n , now total trees =50+n

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
sher mohammad
b.tech, iit delhi