5. Finding new land that supports new state law Inequalities and Equations Used To Graph New Polygon: 12,000,000 ≥ 1,000x + 3000y 2,040,000 ≥ 300x + 400y 10,200 ≥ 2x + y x = 0 y = 0 x + y = 6000 x = 4800 y = 3600 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. New Equations That Represent This State Law: x = 4800 ( For Cotton) y =3600 ( For Pistachios) New Farm Land
6. finding profit equation Profit Equation: 1,500x + 4,000y – 1,000x – 3,000y = Profit ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ Total Profit ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ Acres Of Pistachios ^ ^ ^ ^ ^ ^ ^ ^ ^ Price Per Acre Of Pistachios ^ ^ ^ ^ ^ ^ ^ ^ Subtracting Because You Are Losing Money ^ ^ ^ ^ ^ ^ ^ Acres Of Cotton ^ ^ ^ ^ ^ ^ Price Per Acre Of Cotton ^ ^ ^ ^ ^ Subtracting Because You Are Losing Money ^ ^ ^ ^ Acres Of Pistchios ^ ^ ^ Amount Of Profit For Pistachios Per Acre ^ ^ Acres Of Cotton ^ Amount Of Profit For Cotton Per Acre Simplified Version: 500x + 1,000y = Profit
7. Finding maximum profit using vertices Vertices: (0,3600) #1 (1200,3600) #2 (2640,3120) #3 (3600,2400) #4 (4200,1800) #5 (0,0) #6 (4800,600) #7 (4800,0) #8 ^ ^ ^ ^ ^ ^ ^ ^ < < < Point With The Most Profit 2640 Cotton & 3120 Pistachios For Max Profit ^ ^ ^ ^ ^ ^ ^ ^ ^ < < < < < < < < < < < < < < < Lines Used To Determine This Point: x + 3y + 12000 & 3x + 4y = 20400 Point 1 3,600,000 Point 2 4,200,000 Point 3 4,440,000 Point 4 4,200,000 Point 5 3,900,000 Point 6 0 Point 7 3,000,000 Point 8 2,400,000
8. Time to do some mixing! Equation For Gallons Needed: .54x - .12x +260.256 = 787.968 .42x + 260.256= 787.968 .42x = 527.712 x = 1,256.45714 In conclusion I will have to need approximately 1,256 gallons of herbicide mixed with 54% and 12% glysophate in order to achieve a mixture that is 2,188.8 gallons and 36% glysophate. Total Gallons % Glysophate Pure Glysophate Solution A x 54% .54x Solution B 2,188.8 - x 12% -.12x + 260.256 Mixture 2,188.8 36% 787.968
9. Time to hire some 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? Total Crews Needed: About 32 Crews Rate Time James 1 5 Jose 1 3 Mark 1 2 424,320 424,320 424,320 Total Trees
