Question

Maximizing yield. Hood Apple Farm harvests an average of 30 bushels of apples per tree when 20 trees are planted on an acre of ground. If 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield

Answer 1

In order to get the highest yield, 25 tress should be planted

Explanation:

Given the data in the question;

Let n be number bushel, b is bushels per tree, t is number of trees

from the question, if t = 20, b = 30

and if t = 21 then b = 29

so t + b is constant

t + b = 50 ----- let this be equation

now, n = t × b

so b = n / t

hence from equation, we input b = n/t

t + n/t = 50

n/t = 50 - t

n = t(50 - t)

n = 50t - t²

now we get the derivatives

Note, The maximum amount of trees is simply where the derivative is equal zero, so;

0 = 50 - 2t

2t = 50

t = 50/2

t = 25

Therefore, In order to get the highest yield, 25 tress should be planted