4. Using the Simplex Method, solve: Maximize 5x1+x2 3x12x2 ≤ 6 subject to -401 + 2x2 ≤4 x1, x2 ≥ 0 (ID vita
4. Using the Simplex Method, solve: Maximize 5x1+x2 3x12x2 ≤ 6 subject to -401 + 2x2 ≤4 x1, x2 ≥ 0 (ID vita
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please follow how the example was given in the other photo to solve this LPP using simplex method. This was is easier and short for me to understand
![Put in Standform
Basic feascal Solution
To phase Method
Ex 2: Solve the LP problem weing the simplex
Method:
Max
84:
J
5x + 6x₂
S3x₁ + 4x₂ = 18
2x₁ + x₂ < 7
X₁, X270
Soln: 1st transform the LP problem into standard
form
bv
X3
X4
Construct the initial
Initial
min
5x - 6x₂
& √3x₁ + 4x₂ + x3 = 18
2x₁ + x₂ + x4 = 7
-х, ха, хз, х4 70
X₁
is NOI
-S
X₂
4
Current basis
XB =
b.f.s
1
-6
X3
1
O
Ⓒ
}
000円
tableau
X4
20-0
O
Using the
Simplex Metud
b
18
7
O
[93 94] = [0]
(₂=-6
min
~ { b², 9:₂>0} = min [18, +} = 2
The
two-phase Simplex Method
There are two times when an 4 probleem has no
starting bifis and thus, the simplex method canot
be readily initiated. Thus, there is a need to
a
systemic method to find
LP problem.
The
Two-
Method
an
require
Starting bifs to such
-phase
Such
method
Example: be the simplex method to solve
min
2x₁ + 3x₂
Slo: 1st
Sit
a
4x + 2x₂ > 12
X₁ + 4x₂ > 6
X₁, X₂ 70
transform
min
sit
9 which occurs in
row I
is
the
2x + 3x₂
4рх, +2х2 - Хз
- 12
X₁ + 4x₂ - X = 6
X₁, X2, X3, X470
problem in standard form :
There is
basis matrix since on the f.T-
no
for tp problem would imply there is a bifus. But
Such a Solution would have been (00X3 X4) ! But
X3 = -12 and Xq = -6
which is feasible.
none
of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F4e448421-b01d-4d34-b2ff-ddd8e26e3cd4%2Fvu8c2c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Put in Standform
Basic feascal Solution
To phase Method
Ex 2: Solve the LP problem weing the simplex
Method:
Max
84:
J
5x + 6x₂
S3x₁ + 4x₂ = 18
2x₁ + x₂ < 7
X₁, X270
Soln: 1st transform the LP problem into standard
form
bv
X3
X4
Construct the initial
Initial
min
5x - 6x₂
& √3x₁ + 4x₂ + x3 = 18
2x₁ + x₂ + x4 = 7
-х, ха, хз, х4 70
X₁
is NOI
-S
X₂
4
Current basis
XB =
b.f.s
1
-6
X3
1
O
Ⓒ
}
000円
tableau
X4
20-0
O
Using the
Simplex Metud
b
18
7
O
[93 94] = [0]
(₂=-6
min
~ { b², 9:₂>0} = min [18, +} = 2
The
two-phase Simplex Method
There are two times when an 4 probleem has no
starting bifis and thus, the simplex method canot
be readily initiated. Thus, there is a need to
a
systemic method to find
LP problem.
The
Two-
Method
an
require
Starting bifs to such
-phase
Such
method
Example: be the simplex method to solve
min
2x₁ + 3x₂
Slo: 1st
Sit
a
4x + 2x₂ > 12
X₁ + 4x₂ > 6
X₁, X₂ 70
transform
min
sit
9 which occurs in
row I
is
the
2x + 3x₂
4рх, +2х2 - Хз
- 12
X₁ + 4x₂ - X = 6
X₁, X2, X3, X470
problem in standard form :
There is
basis matrix since on the f.T-
no
for tp problem would imply there is a bifus. But
Such a Solution would have been (00X3 X4) ! But
X3 = -12 and Xq = -6
which is feasible.
none
of
Transcribed Image Text:Using the Simplex Method, solve:
Maximize 5x1 + x2
3x12x26
subject to-4x1+2x2 ≤ 4
x1, x2 > 0
(10210 gast.
V
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