Question

Each orange tree grown in California produces 720 oranges per year if not more than 20 trees are planted per acre. For each additional tree planted per acre, the yield per tree decreases by 15 oranges. How many trees per acre should be planted to obtain the greatest number of oranges?

Answer 1

number of extra trees per acre --- n

number of trees per acre = 20+n
yield per tree = 720 - 15n

number of oranges = N = (20+n)(720-15n)
= 14400 + 420n - 15n^2
N ' = 420 - 30n
= 0 for a max of N
30n = 420
n = 14

for the best yield there should be 20+14 or 34 trees per acre