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Math Partial 1 Project

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by

Luz Paczka

on 19 September 2014

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Transcript of Math Partial 1 Project

Equation
8. An orchard..
presently has 30 trees per acre. Each tree yields 400 peaches. It is determined that each additional
tree that is planted per acre, the yield will be reduced by 20 peaches per tree. How many trees should be added
per acre to maximize the yield?

What is the unknown?
What are the given quantities?
What are the given conditions?
Notations
P(t)= (400-20t)(30+t)
We want to optimize the production of peaches in relation to the number of trees in an acre.
Peach Production
P-Peach production to be maximized when t trees are added.
t-trees
We know, the amount of peaches depends on the amount of trees,therefore, :
t- independent variable
p- dependent variable

THEREFORE:
P(t)=(400-20t)(30+t)
T-CHART
Proving the optimization derivative...
-40t-200=0
-40t=200
t=-5
Derivatives
For our peach production optimization
P'(t)=-40t-200
Math Partial 1 Project
UNKNOWN
Amount of trees we needed to maximize the amount of peaches produced per acre.
GIVEN DATA
Amount of trees per acre:
30 trees
Amount of peaches per tree:
400 peaches
Amount of peaches per tree when there are additional trees (per acre):
+1 tree-20peaches
Conditions

When a tree is added to the acre (having 30 trees), the production of peaches per tree would decrease in 20 peaches.
P(t)= -20t -200t+12000
2
Diana Cristina Castro Armenta A01225990
Luz América Paczka Giorgi A01226178

Group 11
Mathematics AP
Professor: Tiberiu Hrabak

P(t)= -20t -200t+12000
2
P''(t)=-40
P'(t)=-40t-200
P(t)
t
-5
*
P(t)= -20t -200t+12000
2
-8
0
12320
12500
12000
GRAPH
t
p
P(-5)= [400-20(-5)](30-5)
P(-5)=500*25
P= 12500
To prove...
After reading and understanding the problem...
P'(t)
t
-5
-8
0
120
0
-200
Full transcript