Question

The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 900-9n apples. So the number of apples produced per acre is A(n)=n(900-9n)

Answer 1

How many trees should be planted per acre to obtain max yield of apples?

Answer 2

are you doing derivatives yet?

Answer 3

Wouldn't u just set it up as 900-9n=0

Answer 4

This is precalculus

Answer 5

A(n) = n(900-9n) = 900n - 9n^2

Answer 6

that is an expression of a downward facing parabola, so the highest point on the curve is the max for A(n).

You could sketch the curve... you could complete the square and factor. Just depends on what you are comfortable doing.

Once you learn derivatives or differentiation, this problem gets a lot easier.

Answer 7

Wanna show me how to use the derivative to solve?

Answer 8

I know how to take derivatives

Answer 9

oh, sorry... awesome!

Answer 10

derivative of A(n) with respect to n gives you A ' (n)

A(n) = 900n - 9n^2

A ' (n) = 900 - 18n

The max point on A(n) will be a point where the curve tips over the top of the parabola... and the slope at that point will be zero, so you set A ' (n) = 0 and solve for n.

Answer 11

that n that you solve for then gives the max number of trees, n.

If you wanted the max # of apples, use that "n" in the original A(n) function and solve for A(n)