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Grade: 12

                        

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 ?

6 years ago

Answers : (5)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							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
6 years ago
sidduchinnu
37 Points
							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.
						
6 years ago
Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							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

6 years ago
Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							
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
6 years ago
Arun Kumar
IIT Delhi
askIITians Faculty
256 Points
							


Arun Kumar
IIT Delhi
Askiitians Faculty
6 years ago
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