SOLUTION: 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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 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       Log On


   

Question 167426This question is from textbook
: 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. How many pounds is the maximum yield?

I understand the concept of max and min. What I can't get is the quadratic function. This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 = %28-b%29%2F%282a%29
In this problem: a=-4; b=120
x = %28-120%29%2F%282%2A-4%29
x = %28-120%29%2F%28-8%29
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