Consider the problem: Minimize 1-3x2 -0.4x3 3x1₁ - x2 + 2x3 ≤7 -2x1 + 4x2 < 12 -4x1 + 3x2 + 3x3 ≤ 14 X1, X2, X3 ≥ 0 subject to a). Find an optimal solution. b). At most how many optimal basic feasible solutions are there? Show your work.
Consider the problem: Minimize 1-3x2 -0.4x3 3x1₁ - x2 + 2x3 ≤7 -2x1 + 4x2 < 12 -4x1 + 3x2 + 3x3 ≤ 14 X1, X2, X3 ≥ 0 subject to a). Find an optimal solution. b). At most how many optimal basic feasible solutions are there? Show your work.
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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Linear Programming
I attached 2nd photo so you could use structure of that tableau… it’s easier for me to understand. First convert to standard form tho
Transcribed Image Text:2. Consider the problem:
Minimize 1-3x2 -0.4x3
subject to
3x1 - x2 + 2x3 ≤ 7
-2x1 +4x2 < 12
-4x1 + 3x2 + 3x3 ≤ 14
X1, X2, X3 ≥ 0
a).
Find an optimal solution.
b). At most how many optimal basic feasible solutions are
there? Show your work.
Transcribed Image Text:#3 Cont
+ R₂
10
Q
R₁-5R2
R3+10R₂
5R₂
R₁ +422
R3 + 2 R₂
1217
(2 + ² R₁
min -10X₁ - 6x2 +8x3
St.
bv
jX₂
X45
510
X 4
XI
1-10
5
1
Pela
|--10
1
blo
O
5 X ₁-2 X2 +6X3 + xy =
110 X₁ + 4x₂ - 6x3 + x5
X₁1 X21 X 31
X4 X5 20
X41
X1 5/2
0
X4 10
X25/2
5
X4 10/3
X2 5/2
5
X3 10/3
X215
25/3
X₂
-2
니
-6
-2
NOWYJNIN
5
1-4
D
to
-2
-
X3 X4 X5
6
O
0
1
O
1
O
4
-2
0
1
0
9/20
9
1
80
OOOOOOO
0
-3
1
20
91
2
3.
1
- 23/20
1-1
1
30 to 3
30
5
-3/1/20
-bo-o
01/12
32
1
-2/22
= 20
=30
1
21/12
1
ib
20
30
O
20
3
O
i/c
5
15/2
3/2
45
1/3 16 35/3
1/4 15/2
30
35)
O
3/2/45
43 16 35/3
25
½/22
5/3 170/3
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You didn't follow the same structure of the tableau i gave you in 2nd photo. Please refer back to using that structure... I don't understand this
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