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 should be added to the existing orchard in order to maximize the total output of trees
apples = (50+x) (800-10x) find max
40 000 - 500x + 800x - 10x^2
-10 x^2 + 300 x + 40000 max occurs at x = -b/2a = - 300/-20 = 15 additional trees
50 trees + 15 trees = 65 trees output = -10(15^2) + 300 (15)+(40000) = 42250 apples from 65 trees