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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 ?

Grade:Upto college level

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 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
askiitians faculty
IIT Delhi
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 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
sher mohammad
b.tech, iit delhi

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