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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 ?

bharat bajaj IIT Delhi
7 years ago
`The output for x no. of trees is then : (800 - 10n)(50+n)Hence, O = 300n - 10n^2 + 40000Differentiate it :300 - 20n = 0hence, n = 15Hence, 15 trees should be added.ThanksBharat Bajajaskiitians facultyIIT Delhi`
7 years ago
`let number of additional tree is n , now total trees =50+napple production per tree =800-10ntotal production =(50+n)(800-10n)= -(10n^2-300n-40000)f'(n)= 20n-300=0n=15sher mohammadb.tech, iit delhi`