An apple orchard has an average yield of 32 bushels of apples/tree if tree densi
ID: 3187455 • Letter: A
Question
An apple orchard has an average yield of 32 bushels of apples/tree if tree density is 18 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels/tree. How many trees should be planted in order to maximize the yield?Explanation / Answer
take help i solve for 40 bushes and 20trees/acre Total yield = amount of trees * yield per tree yield per tree = 40 bushels per tree (normal conditions) Total yield = (20 trees + amount of extra trees) * (40 bushels per tree - 2 bushels per extra tree) let total yield be Y and extra bushels be X. Then: Y = (20 + X) * (40 - 2X) = 800 - 40X + 40X - 2X^2 = -2X^2 + 800 -------> here you it should be clear that you are working with a parabola Because you are working with -2X^2 (and not 2X^2) you should know that the vertex of the parabola is its maximum value. Now rewrite the function in vertex form: Y = a( x - h )^2 + k where (h,k) is the vertex point Y = -2( X - 0)^2 + 800 therefore (0,800) is the maximum value of the graph. Therefore a maximum yield of 800 bushels can be yielded if 0 extra trees are used. The density of the trees should therefore be 20 trees/acre.