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# LD. 26. Rancher.

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BC: By: Lyndsey Doire Algebra and Trig Period C January 6, 2012 Question 26

FC: Question 26: Rancher By: Lyndsey Doire

1: A rancher wants to yield the maximum amount of edible beef off his square mile of land. At first he finds that as he adds more cattle, his yield goes up. However, if he overgrazes, the harvest goes down. An agricultural agent tells him that his yield will vary quadratically with the number of animals that he grazes. For five head of cattle, his production is 8,750 pounds of beef, and for 10 head, he reaps 15,000 pounds of beef. He had no production when he was grazing no cattle. -Define the variables, write the ordered pairs, and find the equation of this function expressing pounds of beef produced in terms of the number of cattle. -What number of cattle will give him his maximum profit in number of pounds? -What is the maximum weight? -What is the domain and range of this function? Explain your reasoning. -What other factors could affect the amount of edible beef that is produced?

2: 1. Define the variables, write the ordered pairs, and find the equation of this function expressing pounds of beef produced in terms of the number of cattle. | Ordered pairs: (5, 8,750) (10, 15,000) (0, 0) | Equation: y= -50x^2+20000x+0 | Explanation: The y variable represents the pounds of beef. The x variable represents the cattle. (5, 8,750) is an ordered pair because for every 5 cattle there will be 8,750 pounds of beef. (10, 15,000) is an ordered pair because for every 10 cattle there will be 15,000 pounds of beef. (0, 0) must also be an ordered pair because for 0 cattle there will be 0 pounds of beef produced.

3: 2. What number of cattle will give him his maximum profit in number of pounds? | 20 cattle will give the maximum profit in number of pounds.

4: 3. What is the maximum weight? | The maximum weight is 20,000 pounds of beef which is only achievable at 20 cattle.

5: 4. What is the domain and range of this function? Explain your reasoning. | Domain: [0, 20] Range: [0, 20,000] The domain is [0, 20] because if the number of cattle exceeds 20 then the pounds of beef will decrease. The Range is [0, 20,000] because 20,000 pounds of beef is the maximum pounds of beef that can be obtained before it starts decreasing.

6: 5. What other factors could affect the amount of edible beef that is produced? | There could be many factors that affect the amount of edible beef that is produced. If there isn't enough food the animals will starve. If there is too much food the meet could become too fatty. There could be factors that have nothing to do with the number of cows or how much food there is. Possibly there are predators that may attack the cows. People could somehow harm the cows. There are countless ways that would effect the amount of edible beef.

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