Answer:
126 trees should she plant per acre to maximize her harvest.
Step-by-step explanation:
Let x be the additional tress that must be plant after planting 100 tress.
So, total number of trees = 100 + x trees
Also, Each additional tree planted decreases the yield of each tree by 3 bushels.
So , net bushels by each tree = 35 - 3x
The revenue function becomes
f(x) = (100 + x)(35 - 3x)
Thus,
Differentiating it by using chain rule as:
f'(x) = (100 + x)35 + 100(35 - 3x)
f'(x) = 3500 + 35x + 3500 - 300x
f'(x) = 7000 - 265x
<u>For maxima of f(x), f'(x) = 0</u>
7000 - 265x = 0
Thus,
x = 26.4151
<u>Since, x represents tress, so, x is 26.</u>
<u>So, total tress she would plant to earn maximum revenue = 100 + 26 = 126 trees</u>
