Let the following current tableau of a maximization problem with slack variables S1 , S2, S3 . X1 X2 X3 S1 S2 S3 RHS 1 a b 1 d. f n h i 1 k a) In which condition is the tableau optimal? b) If a=-5, b=-3, c=5 which variable will enter the basis? c) Let x2 is entering the basis. In which condition does s2 leave the basis? d) Let x3 is entering the basis and let e,h,k< 0. What type problem is this? e) Let a=0, b=3, c=5, is the solution optimal? If x2 enters the basis does the objective function value change? Why? f) Let x2 is entering the basis and s3 is leaving the basis. Let n=3, o=6 and p=0. In the new tableau it is seen that the value of m is same. Why do you think the objective function value did not improve?

Let the following current tableau of a maximization problem with slack variables S1 , S2, S3 . X1 X2 X3 S1 S2 S3 RHS 1 a b 1 d. f n h i 1 k a) In which condition is the tableau optimal? b) If a=-5, b=-3, c=5 which variable will enter the basis? c) Let x2 is entering the basis. In which condition does s2 leave the basis? d) Let x3 is entering the basis and let e,h,k< 0. What type problem is this? e) Let a=0, b=3, c=5, is the solution optimal? If x2 enters the basis does the objective function value change? Why? f) Let x2 is entering the basis and s3 is leaving the basis. Let n=3, o=6 and p=0. In the new tableau it is seen that the value of m is same. Why do you think the objective function value did not improve?

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let
the following current tableau
of
maximization problem with slack variables
a
S1 , S2, S3 .
X1
X2
X3
S1
S2
S3
RHS
1
a
b
1
d
e
f
h
i
1
k
1
a) In which condition is the tableau optimal?
b) If a=-5, b=-3, c=5 which variable will enter the basis?
c) Let x2 is entering the basis. In which condition does s2 leave the basis?
d) Let x3 is entering the basis and let e,h,k< 0. What type problem is this?
e) Let a=0, b=3, c=5, is the solution optimal? If x2 enters the basis does the objective function value
change? Why?
f) Let x2 is entering the basis and s3 is leaving the basis. Let n=3, o=6 and p=0. In the new tableau it is seen
that the value of m is same. Why do you think the objective function value did not improve?

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