Saint Leo University General Linear and Quadratic Equation Problems

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.

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.
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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
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170%
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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 (-4×4760)
(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 –
>
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