Min x1 + X2 - 4x3Subject toX1 + x2 + 2x3 < 9X1 + X2 – X3 < 2- X1 + X2 + X3 < 4X1, X2 , X3 2 0The optimal tableau for this problem is given;X1X2X3X4X5X6RHS1-4-1-2-17X11-1/31/3-2/31/3X52116.X32/311/31/313/3 a. Suppose that c2 =1 is replaced by -5. What happens to tableau? Is it still optimal?X2 is a nonbasic variable. What happens if we change the coefficient of a nonbasic variable?b. Suppose that C3--4 is replaced by 0. What happens to tableau? Is it still optimal?Xạ is a basic variable. What happens if we change the coefficient of a basic variable?11c. Suppose that the right hand side which is 2 is replaced by 4What is the new values of variables?d. Suppose that a, is changed from 1 to 2 ). What is new y½ in the tableau and what is the reducedcost of x2 now?e. Suppose a new activity x, 20 having c, = -2 and a6= 1 is introduced. What happens ttableau? Isit still optimal?

Name: Min x1 + X2 - 4x3Subject toX1 + x2 + 2x3 < 9X1 + X2 – X3 < 2- X1 + X2
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Description: Min x1 + X2 - 4x3Subject toX1 + x2 + 2x3 < 9X1 + X2 – X3 < 2- X1 + X2 + X3 < 4X1, X2 , X3 2 0The optimal tableau for this problem is given;X1X2X3X4X5X6RHS1-4-1-2-17X11-1/31/3-2/31/3X52116.X32/311/31/313/3 a. Suppose that c2 =1 is replaced by -5. Wha

Given equations:Z = min(x1+x2-4x3)x1+x2+2x3≤9x1+x2-x3≤2-x1+x2+x3≤4

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a. Suppose that c2 =1 is replaced by -5. What happens to tableau? Is it still optimal? X2 is a nonbasic variable. What happens if we change the coefficient of a nonbasic variable? b. Suppose that c3=-4 is replaced by 0. What happens to tableau? Is it still optimal? X3 is a basic variable. What happens if we change the coefficient of a basic variable? c. Suppose that the right hand side which is 2 is replaced by 4 What is the new values of variables?

a. Suppose that c2 =1 is replaced by -5. What happens to tableau? Is it still optimal? X2 is a nonbasic variable. What happens if we change the coefficient of a nonbasic variable? b. Suppose that c3=-4 is replaced by 0. What happens to tableau? Is it still optimal? X3 is a basic variable. What happens if we change the coefficient of a basic variable? c. Suppose that the right hand side which is 2 is replaced by 4 What is the new values of variables?

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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Question

Min x1 + X2 - 4x3
Subject to
X1 + x2 + 2x3 < 9
X1 + X2 – X3 < 2
- X1 + X2 + X3 < 4
X1, X2 , X3 2 0
The optimal tableau for this problem is given;
X1
X2
X3
X4
X5
X6
RHS
1
-4
-1
-2
-17
X1
1
-1/3
1/3
-2/3
1/3
X5
2
1
1
6.
X3
2/3
1
1/3
1/3
13/3

a. Suppose that c2 =1 is replaced by -5. What happens to tableau? Is it still optimal?
X2 is a nonbasic variable. What happens if we change the coefficient of a nonbasic variable?
b. Suppose that C3--4 is replaced by 0. What happens to tableau? Is it still optimal?
Xạ is a basic variable. What happens if we change the coefficient of a basic variable?
11
c. Suppose that the right hand side which is 2 is replaced by 4
What is the new values of variables?
d. Suppose that a, is changed from 1 to 2 ). What is new y½ in the tableau and what is the reduced
cost of x2 now?
e. Suppose a new activity x, 20 having c, = -2 and a6= 1 is introduced. What happens t
tableau? Is
it still optimal?

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