Question

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.
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.
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

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