The number of apples produced by each tree in an apple orcha

The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 900 - 9n apples. So the number of apples produced per acre is A(n) = n(900 - 9n) How many trees should be planted per acre to obtain the maximum yield of apples.

Solution

2.

A(n) = number of produced apples

A(n) = n*(900 - 9n)

A(n) = 900*n - 9n^2

we need to find max yield of apples, so

A\'(n) = 900 - 2*9*n

for max

A\'(n) = 0

900 - 18*n = 0

18n = 900

n = 900/18 = 50

n = 50,

50 apple rtrees must be planted to get maximum apple yield.

Max number of apple will be

A(n) = n*(900 - 9n)

A(50) = 50*(900 - 9*50)

A(50) = 50*450 = 22500