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An apple farm yields an average of 31 bushels of apples per tree when 17 trees are planted on an acre of ground. each time 1 more tree is planted per​ acre, the yield decreases by 1 bushel​ (bu) per tree as a result of crowding. how many trees should be planted on an acre in order to get the highest​ yield?

Respuesta :

zoexoe
There are 31 bushels of apples when the number of trees is 17 but decreases by 1 for each additional tree x:            
              Yield = (17 + x) * (31 - x)                                                                               
                       = 527 - 17x + 31x - x2                      
                       = 527 + 14x - x2
We know that for function f(x), the derivative df(x)/dx is zero at maximum point x. We can take the derivative of the yield then set it to zero to find x:            
              d(Yield)/dx = 14 - 2x                          
                             0 = 14 - 2x                        
                           2x = 14                          
                             x = 7
Therefore there should be 17 + 7 = 24 trees to be planted on an acre in order to get the highest yield.

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