Question

A cherry 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.?

Answer 1

Answer:

  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.