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.
