Acherry farm estimates from past records that if 23 trees are planted per acre, each tree will yield an average of 55 pounds of cherries per season. if for each additional tree planted per acre 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.?

  39

Step-by-step explanation:

Yield goes down 1 lb for each tree over 23 per acre, so the yield per tree as a function of x trees per acre is ...

  yield per tree = 55 -(x -23) = 78 -x . . . . . pounds of cherries

To get the yield per acre, we multiply the number of trees per acre by the yield per tree:

  lb/acre = (x tree/acre)((78 -x) lb/tree) = x(78 -x)

This is a quadratic function that opens downward and has zeros at x=0 and x=78. The vertex (maximum) is on the line of symmetry, halfway between the zeros. The yield per acre will be a maximum when ...

  x = (0 +78)/2 = 39 . . . . trees per acre

39 trees should be planted per acre to maximize yield per acre.

answer: i wpould go with c

step-by-step explanation: