Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method: Solution 60 + 10M 7 20 10 (a) State the current Basic Feasible Solution (BFS) in terms of the variable values and z-value. Basic II z 0 81 0 ΤΙ 1 a3 0 x2 3-M 5/4 1 2 81 0 1 0 0 €2 M-3 1/4 -1 1 a2 a3 3-4M 0 -14 0 0 0 -1 1 (b) Is this tableau optimal? Explain your answer. (c) Suppose that the LP models a maximisation problem. i. Obtain the entering variable. Explain your answer. ii. Obtain the leaving variable. Explain your answer. iii. Based on your answer in (ii), explicitly identify the type of solution for the LP.
Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method: Solution 60 + 10M 7 20 10 (a) State the current Basic Feasible Solution (BFS) in terms of the variable values and z-value. Basic II z 0 81 0 ΤΙ 1 a3 0 x2 3-M 5/4 1 2 81 0 1 0 0 €2 M-3 1/4 -1 1 a2 a3 3-4M 0 -14 0 0 0 -1 1 (b) Is this tableau optimal? Explain your answer. (c) Suppose that the LP models a maximisation problem. i. Obtain the entering variable. Explain your answer. ii. Obtain the leaving variable. Explain your answer. iii. Based on your answer in (ii), explicitly identify the type of solution for the LP.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
Related questions
Question
INTRODUCTION TO OPERATIONS RESEARCH
![Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method:
Basic
x1
X2
81
€2
a2
a3
Solution
2
0
3- M
0
M-3 3-4M 0
60+ 10M
81
0
5/4
1
1/4
4
0
7
1
1
x1
0
-1
0
0
20
2
0
a3
1
-1
1
10
(a) State the current Basic Feasible Solution (BFS) in terms of the variable values and z-value.
(b) Is this tableau optimal? Explain your answer.
(c) Suppose that the LP models a maximisation problem.
i. Obtain the entering variable. Explain your answer.
ii. Obtain the leaving variable. Explain your answer.
iii. Based on your answer in (ii), explicitly identify the type of solution for the LP.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48192b12-15a5-478f-9d42-a36a38795d92%2F772990fc-f980-457c-959c-019d5b0f9def%2Fxivr9mm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method:
Basic
x1
X2
81
€2
a2
a3
Solution
2
0
3- M
0
M-3 3-4M 0
60+ 10M
81
0
5/4
1
1/4
4
0
7
1
1
x1
0
-1
0
0
20
2
0
a3
1
-1
1
10
(a) State the current Basic Feasible Solution (BFS) in terms of the variable values and z-value.
(b) Is this tableau optimal? Explain your answer.
(c) Suppose that the LP models a maximisation problem.
i. Obtain the entering variable. Explain your answer.
ii. Obtain the leaving variable. Explain your answer.
iii. Based on your answer in (ii), explicitly identify the type of solution for the LP.
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