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Question

The number of oranges (O) produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produce 650 – 7n oranges. So the number of oranges produced per acre is O(n) = n( 650 – 7n). What is the maximum yield of the trees 

   (# of oranges), and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number) 

Answer 1

O(n) = n(650 - 7n) = -7n² + 650n

The graph is a parabola opening downward with n-intercepts 0 and 650/7

The max occurs halfway between 0 and 650/7.