SOLUTION: A farmer finds that if she plants 95 trees per acre, each tree will yield 30 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree
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Question 1136923: A farmer finds that if she plants 95 trees per acre, each tree will yield 30 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest?
Give your answer rounded to the nearest whole number. Answer by greenestamps(13203) (Show Source):
The numbers don't seem realistic -- an increase by about 1% in the number of trees per acre results in a decrease of over 10% in the amount of fruit per tree.
Let x be the number of trees per acre she adds; then the number of trees per acre is (95+x) and the yield per tree is (30-4x) bushels. The total amount of fruit in bushels is
The maximum yield is at the maximum of that expression, which is at
So apparently she currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 43.75.
So the number of trees per acre for maximum yield is 95-43.75 = 51.25.
Looking back at the numbers, maybe they ARE realistic. The sharp drop in yield per tree for each added tree in the beginning suggests that the orchard is already very much overcrowded....
