4) Primal problem: Maks. Z= 3x1 + x2 + 4x3 6x1 + 3x2 + 5x3 <=25 3x1 + 4x2 + 5x3 <=20 X1, x2, x3 >=0 Optimum solution tableau of the primal problem is given below (x4 and x5 are slack variables for constraints 1 and 2 respectively): Z X1 X3 X1 0 1 0 X2 2 -1/3 1 X3 0 0 1 X4 1/5 1/3 -1/5 X5 3/5 -1/3 2/5 9153l 673 Çözüm 17 5/3 a) Find the dual optimum solution (dual variables and dual objective value) from tableau. (5 p.) b) If a new decision variable has been added to problem and objective function coefficient is 4 5 2 . 1st constraint coefficient is , 2nd constraint coefficient is for this variable: does the primal optimum solution change, explain? If the optimum solution changes which values in the tableau change, explain? (15 p.)
4) Primal problem: Maks. Z= 3x1 + x2 + 4x3 6x1 + 3x2 + 5x3 <=25 3x1 + 4x2 + 5x3 <=20 X1, x2, x3 >=0 Optimum solution tableau of the primal problem is given below (x4 and x5 are slack variables for constraints 1 and 2 respectively): Z X1 X3 X1 0 1 0 X2 2 -1/3 1 X3 0 0 1 X4 1/5 1/3 -1/5 X5 3/5 -1/3 2/5 9153l 673 Çözüm 17 5/3 a) Find the dual optimum solution (dual variables and dual objective value) from tableau. (5 p.) b) If a new decision variable has been added to problem and objective function coefficient is 4 5 2 . 1st constraint coefficient is , 2nd constraint coefficient is for this variable: does the primal optimum solution change, explain? If the optimum solution changes which values in the tableau change, explain? (15 p.)
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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Transcribed Image Text:4) Primal problem:
Maks. Z = 3x1 + x2 + 4x3
6x1 + 3x2 + 5x3 <=25
3x1 + 4x2 + 5x3 <=20
X1, x2, x3 >=0
Optimum solution tableau of the primal problem is given below (x4 and x5 are slack variables for
constraints 1 and 2 respectively):
Z
X1
X3
X1
0
1
0
X2
2
-1/3
1
X3
0
0
1
X4
1/5
1/3
-1/5
X5
3/5
372
-1/3
2/5
Çözüm
17
5/3
3
a) Find the dual optimum solution (dual variables and dual objective value) from tableau. (5 p.)
b) If a new decision variable has been added to problem and objective function coefficient is
1st constraint coefficient is
4
5
2
, 2nd constraint coefficient is
for this variable; does the primal optimum solution change, explain? If the optimum solution
changes which values in the tableau change, explain? (15 p.)
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