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

 

Lemon Farm In Chiluvuru, Andhra Pradesh

Chiluvuru (also called Chiluvur), a village in Guntur district, is popular for lemon cultivation. Hundreds of hectares of land is occupied with lemon farms. Checkout the photographs below:

Mandi at Tenali is the central point where all the farmers, big and small, sell their produce.  The produce is measured in mandi as Tikki, which is equivalent to 50 Kilograms. Usually, the lemon price varies anywhere between Rs. 400 per quintol (Aproximately US$7 per quintol) up to Rs. 4000 (US$70 per quintol or 70 cents per Kilogram). One quintol is equivalent to 100 Kilograms. On average, farmers get about Rs. 100,000 per year per acre of lemon farm.

The farmers get poor prices many times from local traders who buy lemons at a very cheap rate and sell at a very high price. Though government has promised online marketing for agricultural produce, it has not reached the people so far.

Other varieties that are grown in the village of Chiluvuru are Sapota, vegitables like brinjal, ladies finger, and others.

Indian government digitized the agricultural products data in the country, and you can find the quantity and price of any agricultural produce using this site:

http://www.agmarknet.gov.in/

The temple seen in the background is a centuries old Shiva temple, which a famous visiting spot in Chiluvuru.

Resources:
Link to Lemon exporters from India:
https://www.exportersindia.com/indian-suppliers/lemon.htm