Task #1: Search Google Earth for the perfect piece of land (Any shape other than a rectangle). Once you have found it, take a snapshot of the land in SmartNotebook. Determine the dimensions of the property that would give you your desired acreage. Remember, you must be between 100 and 10,000 acres (round to the nearest 100 acres). Determine the equations that would model the property lines. You may use GeoGebra to help you with this, but you should also demonstrate how you would find those equations algebraically. Equations must be in Standard and Slope-Intercept Form. (Standard 6.0 and 7.0)
Task #2: The bank is willing to loan you $2000 per acre to farm your land. However, cotton costs $1000 per acre and pistachios cost $3000 per acre to farm. Determine how much money you have available for this project. Note: You must first determine how many acres you have to farm. How big is an acre? Look it up!
What inequality can be used to model this situation? (Standard 2.0, 7.0)
Task #3: Because of the high demand on fertilizer and water, you have a limit as to how much of each you can obtain. Your fertilizer supplier can provide you with 340 units of fertilizer per acre and the water district will allot you 1.7 acre-feet of water per acre. Cotton requires 300 units of fertilizer per acre and 2 acre-feet of water per acre. Because the pistachios are well established, they will require more fertilizer but less water. Pistachios take 400 units of fertilizer per acre and 1 acre-foot of water per acre. Write two inequalities for this situation. Let the first inequality represent the amount of nitrogen needed compared to the amount available. Let the second inequality compare the amount of water needed with the amount available. (Standard 7.0)
Task #4: Because of the fact that you will be “changing” an existing piece of land, you will be required to adhere to 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 you are ready to graph your set of linear inequalities. But, before you do, there is one last inequality that you must consider. Is ther a limit to how large x + y can be?GeoGebra doesn't handle inequalities very well so you must turn them into equations in order to graph. Insert your equations into GeoGebra and use what you know about inequalities to determine the shaded region. Use the polygon tool to create the polygon that is determined by the shaded region. (Standard 6.0)
Task #5: How much money can you make? The current selling prices for your crops are as follows:
Cotton: $1500 per acre
Pistachios: $4000 per acre
Write an equation that involves x and y that could be used to determine potential profit.
Task #6: The vertices of your polygon from Task #4 can be used to determine your maximum profit. Use GeoGebra to determine the vertices of your polygon. Once you have found the coordinates of each vertex, substitute the values of x and y into your profit equation to determine potential profits. Which point gives you the most profit? Which lines are used to determine this point? Show how you could have found that point of intersection algebraically. (Standard 4.0 and 9.0)
Task #7: In order to maintain your crop, you must spray an herbicide to control the weeds. Glyphosate is a common herbicide used in agriculture. However, glyphosate can be purchased in different concentrations. A farmer can purchase a solution that is 54% glyphosate but your average homeowner can only purchase solution that is 12% glyphosate. You happen to have thousands of gallons of both available but, new legislation dictates that you can only use a solution of 36% glyphosate. Your job is to determine how many gallons of 54% glyphosate must be mixed with 12% glyphosate in order to obtain a mixture that is 36% glyphosate. The number of gallons of 36% glyphosate is dependent upon the number of acres you will be farming. Keep in mind that you will only be spraying the land that is being farmed and you will use .38 gallons/acre. (Standard 15.0)
Task #8: It is time to start pruning the trees and you hire three new workers. 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? Does this seem reasonable? Why? 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? (Standard 15.0)
Task #9: Create a final proposal justifying how many acres of each crop you will farm. Your proposal should include but is not limited to the following:
- Picture from Google Earth (you imported to GeoGebra) of the land you are purchasing with the lines and equations that determine the borders.
- Budget, Fertilizer, Water, State Law restrictions inequalities.
- Profit equation.
- Picture of your polygon from GeoGebra. Include labels for the points and the equations you use.
- Written recommendation explaining your plan of action. Be sure to give brief explanations behind your conclusions. Your explanations do not have to be long, but they do need to justify your conclusions.
- Your final proposal must be digital and able to be embedded into a webpage. You may use Voicethread, Slideshare, Screencast, Prezi or any other tool agreed upon between you and Mr. Cox.
I don't want this project to be so contrived. I spent a lot of time talking with a friend who happens to be a farmer, so I know that much of the information is reasonable if not accurate. I wonder if this could work if I simply told students to pick choose an amount of acreage, pick two crops and then research the given restrictions. Suggestions?
If you are interested, the project is here.