Number of Lemon Trees To be planted Per Acre

The annual yield per lemon tree is fairly constant at 320 pounds when the number
of trees per acre is 50 or fewer. For each additional tree over 50, the annual
yield per tree for all trees on the acre decreases by 4 pounds due to
overcrowding. Find the number of trees that should be planted on an acre to
produce the maximum yield.
;
Let x = no. of trees, over 50, planted
Then y = total yield per acre
:
total yield = No.of trees * lbs of lemons per tree
:
y = (50+x) * (320 - 4x)
FOIL
y = 16000 - 200x + 320x - 4x^2
The quadratic equation
y = -4x^2 + 120x + 16000
:
The axis of symmetry will be the value of x for max y
The formula for that: x =
In this problem: a=-4; b=120
x =
x =
x = +15 trees over 50 (65) gives max yield per acre
:
How many pounds is the maximum yield?
:
you can find that, substitute 15 for x in the quadratic equation 

 

Source: https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.167426.html