here are 50 apple trees in an orchard. Each tree produces 1350 apples. There is

Question

here are 50 apple trees in an orchard. Each tree produces 1350 apples. There is a limited amount of water that is used for irrigation. Because of this, for each additional tree planted in the orchard, the output per tree drops by 12 apples. The owner of the orchard is considering planting more trees, but is concerned that if she plants too many, that overall production will drop. How many trees should be added to the existing orchard in order to maximize the total output of trees ? Production = Number of Trees * Output Per Tree Let x = The Number of Trees that will be Added to the Orchard Number of Trees =( 50 + x ) Output Per Tree = ( 1350 - 12x )

Explanation / Answer

total output = ( 50 + x ) * ( 1350 - 12x ) = 50 * 1350 + 750 x - 12 x^2 differentiate and find min x 750 - 24x = 0 x = 750/24 31.25 = 31 more tress to be added

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