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
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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
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
Using the Simplex Method, solve:
Maximize 5x1 + x2
3x12x26
subject to-4x1+2x2 ≤ 4
x1, x2 > 0
(10210 gast.
V
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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