Michael Rose wants to plant apple trees with the intention of selling the apples

Question

Michael Rose wants to plant apple trees with the intention of selling the apples. He has been told that if he plants 20 trees, he will get 30 bushels of fruit from each tree. However, every additional tree planted will cause competition for water and nutrients among each the trees and will result in an orchard-wide drop in yield of one bushel of apples (i.e, a drop of one bushel for all the trees, not just the extra ones). How many trees should Michael plant to get the greatest amount of fruit? SHOW WORK!

Explanation / Answer

1 tree--->30 bushels. if (20+x) trees---->(20+x)(30-x) bushels. hence to maximise (20+x)(30-x).we take the function F=(20+x)(30-x),dF/dx=0 hence 30-x -20-x=0 hence x=5. Hence he should plant 25 trees in the whole to get the maximum yield

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