Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be
Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
an animal breeder wants to create four identical adjacent rectangular pens, with a total area of 240m^2. To ensure that the pens are large enough for grazing, the minimum for either dimension must be 10m. Determine the dimensions for the pens in order to keep the amount of fencing used to a minimum.
(This is a calculus optimization problem so please show all steps on paper and include the chart of the first derivative test JUST LIKE THE EXAMPLE I AM GIVING YOU HERE)
Transcribed Image Text:Optimization problem are all about realizing the best possible outcome in a situation, subject to a
identify the absolute maximum or minimumAKAST
SELE OUTCO
derivative equ
can
can occur at the endpoints of an interval, or at points for which
1. Draw a diagram label variables and constants.
2. Define: Ovanables (with units) quantity to
be maximized or minimized (with units).
3. Write a fonction for the quantity and define a
closed interval for the function.
4. Differentiate the function.
3. Let dy - and solve Use PDT.
6. Find the y-coordinates for the endpoints of the
interval value that make - Contical valves)
7. Therefore statemenil.
Ex. 1 Three sides of a rectangular field
fenced in with 400 m offencing. Find the dimensions
x
x
Let x represent the width of the enclosure, in metres, x70
Lety represent the length of the enclosure, in metres, yoo.
P=2x+y₁
400=2x+y
400-2x=4
A= xy.
Subin
A= x(400-2x)
= 400x-2x²
dA
όχι
400-47
set dA-O
όχ
0=400-4
FDT
100 = x
fox)
fox)
αA
Interval
Solh
Ford
ax
14100
+
>
x=100
N/A
max.
07100
-
<0
Sub x=100 to ①.
y=400-2(100)
= 00
the dimensions of the rectangle would be
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