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Grade 12Integral Calculus

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 ?

raju

12 Years agoGrade 12

5 Answers

bharat bajaj

Approved Tutor Answer12 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

sidduchinnu

12 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.

Sher Mohammad

12 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

Sher Mohammad

12 Years ago

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

Arun Kumar

12 Years ago

$A_{n}=(50+n)(800-10n)\,\,\,\,\,\,where\,n\,no.\,of\,extra\,tree\,planted\\ =>\frac{\mathrm{d} A_{n}}{\mathrm{d} n}=800-10n-10(50+n)\\ =>n=15\\$

Arun Kumar

IIT Delhi

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