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

Question

bharat bajaj · Answer

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
askiitians faculty
IIT Delhi

Sher Mohammad · Answer

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

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

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

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