Question

A commercial cherry grower estimates from past records that if 20 trees are planted per​ acre, then each tree will yield an average of 36 pounds of cherries per season.​ if, for each additional tree planted per acre​ (up to 25​), the average yield per tree is reduced by 1​ pound, how many trees should be planted per acre to obtain the maximum yield per​ acre? what is the maximum​ yield?

Answer 1

• 28 trees per acre
• 784 lbs per acre

Explanation:

If x is the number of trees planted per acre, we are told the yield per tree is ...

36 -(x -20) = 56 -x . . . lbs

The total yield per acre is the product of the number of trees and the yield per tree:

y = x(56 -x)

This function describes a parabolic curve with zeros at x=0 and x=56. The curve opens downward, so will have its peak value halfway between these zeros, at x = (0 +56)/2 = 28.

28 tree per acre should be planted to maximize yield.

That yield will be (28)(56 -28) = 784 pounds per acre.

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Additional comment

We have to assume that the remark "up to 25" refers to additional trees per acre, rather than the total number of trees per acre.