Question

g An apple grower finds that if she plants 40 trees per acre, each tree will yield 250 bushels of apples. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 5 bushels. How many trees should she plant per acre to maximize her harvest

Answer 1

Answer:

5

Step-by-step explanation:

Number of additional trees is $x$

From the question we formulate the function

$f(x)=(40+x)(250-5x)\\ =-5x^2+50x+10000$

Differentiating with respect to $x$ we get

$f'(x)=-10x+50$

Equating with zero

$0=-10x+50\\\Rightarrow x=\dfrac{50}{10}\\\Rightarrow x=5$

Double derivative of the function we get

$f''(x)=-10<0$

So, at $x=5$ the function is maximum.

So, 5 trees needs to planted per acre in order to maximize her harvest.