Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. This is in order to gain credit even if the final answer is incorrect. 1. maximize 2x1 + 3x2+5x3+x4 subject to x1+x2+2x3 + x4 ≤2, 3x12x2+2x3 + x4 ≤7, 3x2+3x33x4 ≤6, X1, X2, X3, X4 ≥0
Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. This is in order to gain credit even if the final answer is incorrect. 1. maximize 2x1 + 3x2+5x3+x4 subject to x1+x2+2x3 + x4 ≤2, 3x12x2+2x3 + x4 ≤7, 3x2+3x33x4 ≤6, X1, X2, X3, X4 ≥0
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:Solve the following linear program using the simplex algorithm. You should give the
initial tableau and each further tableau produced during the execution of the algorithm.
If the program has an optimal solution, give this solution and state its objective value. If
it does not have an optimal solution, say why.
You should indicate the highlighted row and columns in each pivot step as well as the
row operations you carry out. This is in order to gain credit even if the final answer is
incorrect.
1.
maximize
2x13x2+5x3 + x4
subject to
x1+x22x3 + x4 ≤ 2,
3x2+3x33x4≤6,
3x1 + 2x2 + 2x3 + x4 ≤7,
x1, x2, x3, x4≥ 0
2. Suppose that we are carrying out the simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we
have reached a point where we have obtained the following tableau. Apply one more
pivot operation, indicating the highlighted row and column and the row operations
you carry out. What can you conclude from your updated tableau?
x1 X2 x3
$1
82 83 S4
S1
-2 0
82
3 0 -2
12
1 1
0
0
0
3
0
1
2
0
6
X2
1 1
-3
0
0
1
0
2
S4
-3 0
2
0
0
-1
1
4
-2
-2 0 11 0 0 -4
0
-8
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