Question

An apple farm yields an average of 43 bushels of apples per tree when 23 trees are planted on an acre of ground. Each time 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

Explanation:

Equation of the yield

Yield = Bushels per tree * number of trees

Bushels per tree = 43 when the number of trees is 23 and decreases by 1 for each additional tree

Let n = number of trees

Bushels per tree = 43 when n = 23.

So, bushels per tree = (66 - x)

= (66 - 23)

= 43

Yield = (66 - n) * n

Yield = 66n - n2

Taking the derivative,

66 - 2n

set this to zero to find the maximum 66 - 2n = 0

2x = 66 and x = 33

Maximum yield will be given with 33 trees.

To test 33, 34 and 35 to see that all their yield is less,

yield = (50 - 35)35

= 1085

yield = (50 - 34)34

= 1088

yield = (50 - 33)33

= 1089