An orchard owner has determined that if 20 orange trees are planted pet acre each tree produces about 200 oranges.

Question

An orchard owner has determined that if 20 orange trees are planted pet acre each tree produces about 200 oranges. For each additional tree planted, the yield is decreased by 5 oranges per tree. If x represents the number of additional trees per acre to plant, how many trees per acre should be planted for maximum yield and what would be the maximum yield per acre?

Answer 1

(20+x)(200-5x)=0

4000+200x-100x-5x²=0

4000+100x-5x²=0

this is a parabola that opens downward so its vertex is the maximum point, (h,k) where h=-b/2a

-b/2a=-100/-10=10 trees should be planted for maximum yield

maximum yield:

(20+10)(200-5*10)

30*150=4500 oranges

if you plant 9 trees..

(20+9)(200-5*9)=29*155=4495 which is less oranges

if you plant 11 trees...

(20+11)(200-5*11)=31*145=4495 which again is less

maximum yield again comes from planting 10 more trees to yield 4500 oranges