The Farming Project
Say you inherit a plot of land that's 200 acres. What would the dimensions be? What equations would represent the dimensions?
If the bank is willing to loan you $2,000 per acre, you can get $400,000 in total. Cotton (x) costs $1,000 to farm and pistachios (y) cost $3,000 to farm.
Bank Loan:
1,000(x) + 3,000(y) ≤ 400,000
We need to find out how much fertilizer and water we can get for our land.
Since we have 200 acres of land, we can get 68,000 units of fertilizer and 340 acre-feet of water.
Fertilizer:
300(x) + 400(y) ≤ 68,000
Water:
2(x) + y ≤ 340
A new law has been passed that says cotton can't take up more than 80% of your land and pistachios can't take up more than 60% of your land. We need to find out how much land each crop can take up.
Cotton (x) can take upto 160 acres and pistachios (y) can take upto 120 acres.
Cotton:
0 ≤ x ≤ 160
Pistachios:
0 ≤ y ≤ 120
Total Land:
x + y ≤ 200 acres
Now we need to find out how much profit we're going to make.
Cotton sells for $1,500/acre.
It takes $1,000 to farm it.
Profit = $500
Pistachios sell for $4,000/acre.
It takes $3,000 to farm it.
Profit = $1,000
To find our profit, we can use the equation:
500(x) + 1,000(y) = PROFIT
After findng out how to get our profit, we need to find out how much of each crop to farm to get the maximum profit.
Using the profit equation, 500(x) + 1,000(y) = PROFIT, and using the vertices of the polygon as x & y, we can find out which point will give us the maximum profit.
The point that would give us maximum profit is (88,104).
We need to farm 88 acres of cotton and 104 acres of pistachios to get maximum profit.
In order to maintain our crop, we need to spray glyphosate, a herbicide, to control weeds.
If solution A is 54% glyphosate and solution B is 12%, how much of each should be mixed to get 72.96 gallons of a solution that is 36% glyphosate?
Solution A: 41.6914 gallons
Solution B: 31.2686 gallons
Now we're ready to start pruning our trees.
We need to find out how many 3 man crews we need to hire to prune the trees on our land.
It takes 1 crew 131.6 minutes to do an acre.
The crew will be working 216 hours or 12,960 minutes.
One crew can do 99 acres.
104 acres of pistachio tree divided by 99 acres per crew ≈ 1.05
We would need 2 crews to prune the land.
By: Anmol Khowaja
Period 4-5
