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Answer:
5 more than 30 trees should be planted, for a total of 40 trees per acre.
Step-by-step explanation:
Let x be the number of trees beyond 30 that are planted on the acre
The number of oranges produced = Oranges(x) = (number of trees) (yield per tree)
We are given that For each additional tree in the acre, the yield is reduced by 7 oranges per tree
So, number of oranges produced =
=
=
The derivative Oranges'(x) = 100-20x
Substitute first derivative equals to 0
Using the second derivative test,
Oranges"(x) = -20
20 is negative,
So, this is the case of maximum.
Thus, 5 more than 30 trees should be planted, for a total of 40 trees per acre.