An apple orchard yields 20 bushels of apples per tree when there are 75 trees per acre. For each additional tree per acre, it is estimated that yield will decrease 3 bushels per tree. How many trees should be planted per acre to maximize the yield? Round to the nearest tree.

Answer 1

If there are x additional trees, then the yield is 20-3x per tree
So the total yield is
(75+x)(20-3x)
Now just find the vertex of that parabola as usual.
Hmmm. I suspect a typo, since after only 7 additional trees, the yield per tree will be negative.

Answer 2

present yield: 20 bushels per tree
present number of trees: 75 per acre
income = 20(75) = 1500 bushels

Let the number of additional trees planted be n
yield = 20 - 3n, (20-3x > 0) ----> n < 20/3
number of trees = 75+n

income = (20-3n)(75 + n)
= 1500 - 205n - 3n^2

using Calculus:
d(income) = -205 - 6n
= 0 mor a max income
6n = 205
n = appr 34.2
But that makes no physical sense, the yield would be negative number of bushels

looking at the graph of income = (20-3n)(75+n) shows that the current situation gives
you the maximum yield, unless you take away trees
https://www.wolframalpha.com/input/?i=plot+y+%3D+%3D+%2820-3x%29%2875+%2B+x%29

eg
n trees yield income
1 75 20 1500
2 76 17 1292
3 77 14 1078
-1 74 23 1702