Agriculture The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 900 − 9n apples. So the number of apples produced per acre is
How many trees should be planted per acre to obtain the maximum yield of apples?
To evaluate: The number of trees should be planted per acre to obtain the maximum yield of apples.
Answer to Problem 69E
The number of trees should be planted per acre to obtain the maximum yield of apples is
Explanation of Solution
Given:
The number of apples produced per acre is given by the function
Calculation:
The function of the number of apples produced per acre is given by
The standard form of function,
The maximum or minimum value of the function occurs at,
If
If
From the equation (1) and (2),
Substitute
The number of trees per acre is
The function has maximum value,
Thus, the number of trees should be planted per acre to obtain the maximum yield of apples is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition