The document summarizes the steps taken to maximize profit from a cotton and pistachio farming operation within given constraints. It establishes inequalities to determine the maximum acres of each crop that can be grown within budget, fertilizer, and water limits. It then calculates the profits from cotton at $500/acre and pistachios at $1000/acre to determine a total net profit of $518,000 can be achieved by growing 308 acres of cotton and 364 acres of pistachios.

1. 9 10 5280 ft 5280 ft 3664 ft 1616 ft 1616 ft 6896 ft 1 mile = 5,280 ft 3/4 mile = 3,960 ft 1/2 mile = 2,640 ft 1/4 mile = 1,320 ft y = 8 x = 8 + 2.224 y = 2.224 x = 8 x = 2.224 y = 8 - 2.224 1 mile = 8 spaces 3/4 mile = 6 spaces 1/2 mile = 4 spaces 1/4 mile = 2 spaces 43, 560 sq ft = 1 acre On a graph for every two spaces it equals 1/4 of a mile. When we have (for example) the equation x = 8+ 2.224 it shows by the 8 that we have one mile then the 2.224 we have a little over 1/4 of a mile. That side of the property would be a little over a mile and a fourth.

2. Budget Inequality - $1,400,000 is less than or equal to $1,000x + $3,000y Fertilizer Inequality- 23800 is less than or equal to 300x + 400y Water Inequality-1190 is less than or equal to 2x + y State Law Restrictions- x is less than or equal to 560 y is less than or equal to 420 Pr ofit Equation - $500x + $1000y = profit

3. x + 3y = 1400 maximum amount of money the bank will loan you 3x + 4y + 2380 amount of fertilizer 308 = acres of cotton 364 = acres of pistachios

4. During this project our goal was to figure out how many acres of pistachios and cotton we could farm while making a maximum profit out of them. (x = cotton, and y =pistachios) First I had to find out how much money I had available for this project. The bank will loan me $2000/ac for a total of $1,400,000. Cotton cost $1000/ac to farm and pistachios cost $3000/ac to farm. By using this information I came up with the inequality of $1,400,000 is less than or equal to $1000x + $3000y. This will help me find out how much money I will be using for cotton and pistachios without going over my limit. Second I had to make an inequality for how much water and fertilizer I could obtain. The fertilizer company will provide me with 340 units of fertilizer per acre. The water company will give me 1.7 acre feet of water per acre. Cotton takes 300 units per acre of fertilizer and 2 acre feet of water per acre. Pistachios require 400 units of fertilizer per acre and 1 acre foot of water. First I multiplied 1.7 by 700 = 1190 acft, to see how much water I will be supplied for the season. Then I multiplied 340 units by 700 acs = (238,000 units) to see how much fertilizer I will be receive. Now we can write the inequality 238,000 units is less than or equal to 300x + 400y to find out our fertilizer. Water allotment is1190 acft of water is less than or equal to 2x + 1y acft of water. I now know how much water I can use without going over my allotment. Third, due to a new state law pistachios cannot take up more than 60% of my land and cotton cannot take up more than 80% of my land. Multiply 700 by .8 and 700 by .6 to get x is less than or equal to 560 acs (cotton) and y is less than or equal to 420 acs (pistachios). Refer to slide #3 to see how I was able to get my acres of cotton (308/acs) and pistachios (364/acs) by plugging in the equations I have made. Fourth, crops are selling at a rate of $1500/ac for cotton and $4000/ac for pistachios. Since the bank loaned me $1000/ac for cotton and $3000/ac for pistachios I have to subtract that from my earnings to show a net profit. So my equation will look like this: 500x + 1000y = net profit. There are other factors that account in farming such as pruning or herbicides. These tasks which were done by using percent and rate mixer problems. They were great to know but didn't influence my net profit since my expenses where fixed through the bank loan. If these expenses would have reduced my bank loan they would have been a factor in my net profit. By working through these steps I have found through my equations that I will be making $500/ac on cotton and $1000/ac on pistachios. I am farming a total of 308 acres of cotton and 364 acres of pistachios. Therefore I will show a profit of $154,000 on cotton and $364,000 on my pistachios. Equaling a net profit of $518,000. (I've really enjoyed working on all these Tasks and have learned a lot. Maybe now I will be able to help my Dad on the farms. Thanks Mr Cox)