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)

Question

anonymous · Answer

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

anonymous · Answer

are you doing derivatives yet?

anonymous · Answer

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

anonymous · Answer

This is precalculus

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

Wanna show me how to use the derivative to solve?

anonymous · Answer

I know how to take derivatives

anonymous · Answer

oh, sorry... awesome!

anonymous · Answer

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.

anonymous · Answer

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)