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...
Related questions
Question
in his model for storage and shipping costs for a manufacturing process, a researcher develops the following formula c=100(100+9x+144/x), where C is the most storage and transportation for up to 100 days of operation and load of material is moved every "x" days. Find the value of x for which C is a minimum.
(This is a calculus optimization problem, please show all work and add the chart for the first derivative test just like this example I am giving here, do the work like the example and put that chart too)
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning