Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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](https://content.bartleby.com/qna-images/question/79599c56-a340-49a0-b0ff-829b3947a798/4e448421-b01d-4d34-b2ff-ddd8e26e3cd4/vu8c2c_processed.jpeg)
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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