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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

 Mar 12, 2020
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apples =   (50+x) (800-10x)    find max

                40 000 - 500x + 800x - 10x^2

                 -10 x^2  + 300 x + 40000                    max occurs at x = -b/2a =   - 300/-20 = 15 additional trees

 

50 trees + 15 trees = 65 trees      output =  -10(15^2) + 300 (15)+(40000) = 42250 apples from 65 trees

 Mar 12, 2020

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