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 should be added to the existing orchard in order to maximize the total output of apples?

Answer 1

call x the number of trees to add
you will have (50+x) trees in the orchard

each tree produces 800 apples, but this goes down by 10 for every new try
in other words, each tree will produce 800 - 10x apples

total number of apples = # of trees times apples per tree
= (50+x)(800-10x)

that is a parabola, and will have a max at its vertex
or use calculus.. find the derivative, set = to 0, and solve for x.

Answer 2

thanks!

Answer 3

Ok so the derivative of that junk is \[-20x+300\] i think so if i set that to 0 and solve for x i get the answer? @phi
so x = 15?

Answer 4

yes, looks good.