The Farming Project
The Farming Project
By: Fareen Baloch
So What is This About?
In order to do so, you must consider the following:
- How much does each crop cost to farm (per acre)? And how much money is the bank willing to loan you per acre?
- How much money can be made per acre? Keep in mind that one crop may demand a higher price, but may cost more to farm.
- What are you limitations on this 100 acres of land? And how much is needed? [fertilizer, water, people you can hire, money]
These are the dimensions of the piece of land that would give you 100 acres. There are also the equations that represent the dimensions.
Remember!
Bank Loan: $2,000/acre to farm your land.
Cotton costs $1000/acre and pistachios cost $3,000/acre to farm. How much money do you have?
What inequality can be used to model this situation?
$2,000/acre to farm land.
- We have $20,000.00!
1,000x+3,000y≤$200,000
You need fertilizer and water for your farm. Your fertilizer supplier can only obtain you with 34,000 units of fertilizer and the water district will give you 170 acre-feet of water.
Cotton: 300 units of fertilizer/acre and 2 acre-feet of water/acre. Pistachios: 400 units of fertilizer/acre and 1 acre-foot of water/acre.
Write two inequalities for this situation.
First inequality: represent the amount of fertilizer needed compared to the amount available.
Second inequality: compare the amount of water needed with the amount available.
Fertilizer Inequality:
300x+400y ≤34,000
Water Inequality:
2x+1y ≤170
A new state law that states that pistachios cannot take up more than 60% and cotton cannot take up more than 80% of your land.
Write a set of inequalities that model this.
Now graph your set of linear inequalities.
Also, is there a limit to how large x + y can be?
How much money can you make?
Write an equation that involves x
and y that could be used to determine
potential profit.
Selling Prices:
Cotton: $1500/acre
Pistachios: $4000/acre
The vertices of your polygon from Task #4 can be used to determine your maximum profit. Then substitute the values of x and y into your profit equation to determine which point gives you the most profit. Which lines are used to determine this point?
Plug these numbers into this equation:
$500x+$1,000y=t [total profit]
The lines for water and fertilizer determine Point H.
Glyphosate can be purchased in different concentrations. A farmer can purchase a solution that is 54% glyphosate but average homeowner can only purchase solution that is 12% glyphosate. You have thousands of gallons of both available but, new law says that you can only use a solution of 36% glyphosate.
Determine how many gallons of 54% glyphosate must be mixed with 12% glyphosate in order to obtain a mixture that is 36% glyphosate.
A=21. 7 gallons
B=16.3 gallons
James can prune a tree in 5 minutes, Jose can prune the tree in 3 minutes and Mark can prune a tree in 2 minutes. If you have 136 trees per acre, how long will it take them to prune all the trees?
How many 3 man crews (working at the same rate) would you need to hire in order to get the work done in four 54-hour work weeks?
234/16=1.08 crews
You need 2 crews!
Congratualtions!
The End.
You have sucessfully farmed 1oo acres of pistachios and cotton!
You just used math in the real world!
Task 3
What to do?
500x+1,000y= TOTAL PROFIT
Task 5
You need to spray herbicide!
Glyphosate=Common Herbicide
Total Gallons
A= x
B=38-x
Mixture=38
Task 7
- If you have the choice between cotton and pistachios, how many acres of each do you farm?
- Suppose you have inherited a plot of land that is 100 acres. Your job is to go through the following tasks to determine how you can maximize your profit, how much money you need, how many people you should hire, etc.
% of Glysophate
A= 54%
B= 12%
C= 36%
Pistachio Tree
Pure Glysophate Equation:
A=.54x
B=4.56-.12x
Cotton Plant
Mixture= 13.68
.54x+(4.56-.12x)=13.68
Task #1
X=21.7
A= 21.7
B=38-(21.7)
What to do?
Measured in Feet
Task 8
hello
1 tree= 1.03 minutes
1/5+1/2+1/3= x/30
13,600 · 1.03=14,053.33 minutes [234 hours] to prune 13,600 trees
6/30+15/30+10/30=31/30 minutes
31/30=1.03
The farm is 100 acres!
What to do?
Task #2
Task 6
x= number of acres of cotton
y= number of acres of pistachios
Here are the Intersection Points:
I: (70,30)
E: (80,10)
D: (80,0)
B: (0,60)
G: (20,60)
H: (44,52)
F: (60,40)
- 1 acre=40 ft · 1,089 ft or 43,560 ft ²
Point H
$500(44)+$1,000(52)=t
$22,000+$52,000=$74,000
Point H gives you the most profit.
[$74,000]
What to do?
Task 4
Here are the Intersection Points:
B: (0,60)
G: (20,60)
H: (44,52)
F: (60,40)
I: (70,30)
E: (80,10)
D: (80,0)