Acommercial 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?

Step-by-step 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.

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

24

step-by-step explanation: