Question

There are 50 apple trees in an orchard. each tree produces 800 apples. for each additional tree planted in the orchard, the output per tree drops by 10 apples. how many trees in the orchard will yield the maximum output of apples?

Answer 1

apples = (50+x)(800-10x)
       = (40000-500x+800x-10x^2)
       = -10x^2 +300x + 40000
       Max occurs when x = -b/(2a) = -30/(-2) = 15
       = -x^2 + 30x + 4000
       Max occurs when x = -b/(2a) = -30/(-2) = 15
       15 trees should be added