Saint Leo University General Linear and Quadratic Equation Problems

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lhyvffni

Mathematics

Saint Leo University

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Below I have put the parts of this queston that I need help in. I did the work I need help explaining why I got my answer.

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of this project. T Tuesday, April 6th by 11:59pm on Courses. This is the due date for the final project. Your completed project should be written as a letter to the farmer and must contain all of the following parts for full credit. You must begin by summarizing the farmer's predicament in your own words (what problem are you attempting to help him solve and what details were needed to solve it?). This will provide context for the remainder of your letter. Then you should explain how you went about solving the problem for him. While you may include some calculations here (or in an appendix of calculations at the end of the letter), you need to make sure to explain what you did and why you did it. This will minimally require the introducing the function you developed and specifically defining all variables you used. If he next wants to do a similar thing for his lemon or grapefruit grove, you should provide him with enough information so that he would be able to answer the problem himself without bothering you for help. Your letter must be written in complete sentences with appropriate grammar and correct spelling for full credit. When using Microsoft Word, you should include and equations/formulas by using Equation Editor. You can find this either under the Insert tab, or by pressing Alt+= on your keyboard on a PC. Then typing x^2 and pressing space converts it nicely into x2, etc. AutoSave OFF ños 5 W 2021 Spring 151 Writing Assignment Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments v 11 v Evvv Paste V V Normal No Spacing Heading 1 Heading 2 Title Subtitle Styles Pane Dictate Sensitivity Dear College Algebra Students- I'm hoping that you can help me with a decision my family has been struggling with. We own a large and expanding citrus farm and have decided to dedicate an additional acre of farmland for more orange trees but aren't sure how many to plant. If we plant the trees too close together the branches will all run into each other and hurt the overall yield of oranges from the tree, but if we plant them too far apart, then we would be wasting the farmland; each tree would be bursting with lots of oranges, but there may not be enough trees to make it worthwhile. I know there must be an optimal number of trees that we could plant in this area, but I'm not sure how to find it other than trial and error which is very expensive and time consuming. Dr. Murphy has graciously volunteered your help as he mentioned that you have been practicing optimization in class. I have collected data from our other groves and hope that you can find something in here that will help me choose a strategy before I plant. Y On our main field we plant 75 trees per acre and have found that each tree produces an average yield of 460 oranges. We have tried planting both more and less trees in different parts of our farm and have noticed that for each additional tree we plant in the same acre, the average yield per tree ends up dropping by about 4 oranges per tree. This got me thinking that there must be some number of trees to plant that should give me a maximum total yield of oranges. Please help me find the number of trees we should plant on this land. I know that each acre on our main field provides us with about 34,500 oranges, so please also let me know how many oranges I should expect to get from this new acre if I plant according to your recommendations. I simply need the number of trees to plant and I'll worry about how to space them appropriately to fit with our irrigation. Sincerely, Tripp E. Cana TM CEO, Orange Is The New Apple 345 Orchard Lane Citrus Grove, FL 51213 + 170% 1 Focus ERE 1161 words [X English (United States) MacBook Pro 3:02 Maria Marcelina Want: Most oranges Have: 75 trees, 460 orange/tree, to orange. I tree (Stpe mista yield: inumber of trees, number of orange • o y imx + b xy Total yield- T = Xo y = T= Xoy •. 751460 76/456 -4x + 760 X 76-79 Max Vertex za 760 = b y = My = 456-460-L-u T(x) = x (-4x4760) (TG) = -4x²+2608 m X=-b yunon** ---760-(95 4 Number of trees 2(-4) : 95(-4(95) + 760) = 95 (380) - 236.100] 4 Number of oranges By planting 95 Frees, you . should get 36.100 oranges - > 1/1
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Dear Tripp E. Cana
Hi Mr. Cana, your family no longer has to struggle with that decision. You are planning to
dedicate an additional acre of farmland to plant orange trees and need to know how many trees
to plant to maximize the production of the orange by an acre of farmland used. You explained to
us that each orange tree needs a certain farmland space because if they get too close to each
other the branches will run into each other and hurt the overall production and if they are too far
apart you would be wasting farmland and the production would not be enough to make it
worthwhile, even though the trees would be bursting with lots of oranges.
To solve your problem an optimal number of trees is n...


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