Consider the following linear programme L. maximise -6x1 + 5x2 + 3x3, subject to Applying the simplex method to the following final tableau is obtained. (You do not have to verify this.) X1 2x1 + 2x2 + 5x3 ≤ 38, 2x12x2 + 3x3 ≤ 49, -2x1 + x2 + 2x3 ≤ 8. X1 ≥ 0, x₂ > 0, X3 ≥ 0. 1 0 0 0 X2 X3 S1 52 53 0 0 -1 11 0 1 0 87 1 0 1 30 0 9 0 1 81 8 1 3 1 2 Use this tableau to answer the following questions. (a) Write down the solution of L. (b) Find the solution to the linear programme obtained from L by changing the objec- tive function to -6x₁ + 5x2 + 13x3.
Consider the following linear programme L. maximise -6x1 + 5x2 + 3x3, subject to Applying the simplex method to the following final tableau is obtained. (You do not have to verify this.) X1 2x1 + 2x2 + 5x3 ≤ 38, 2x12x2 + 3x3 ≤ 49, -2x1 + x2 + 2x3 ≤ 8. X1 ≥ 0, x₂ > 0, X3 ≥ 0. 1 0 0 0 X2 X3 S1 52 53 0 0 -1 11 0 1 0 87 1 0 1 30 0 9 0 1 81 8 1 3 1 2 Use this tableau to answer the following questions. (a) Write down the solution of L. (b) Find the solution to the linear programme obtained from L by changing the objec- tive function to -6x₁ + 5x2 + 13x3.
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:Consider the following linear programme L.
maximise -6x1 + 5x2 + 3x3,
subject to
2x1 + 2x2 + 5x3 ≤ 38,
2x12x2 + 3x3 ≤ 49,
-2x1 + x2 + 2x3 ≤ 8.
X₁ ≥ 0, x₂ > 0, X3 ≥ 0.
Applying the simplex method to the following final tableau is obtained. (You do not
have to verify this.)
X1 X2 X3 S1 52 53
1
0
0
0 8
0
1
0
0 9
1
3 1
2
0 -1 11
1 0 87
0-1 30
0 1 81
Use this tableau to answer the following questions.
(a) Write down the solution of L.
(b) Find the solution to the linear programme obtained from L by changing the objec-
tive function to -6x₁ + 5x2 + 13x3.
(c) For & ER, suppose the right hand side of the first constraint of L is changed to
38 E. Find the possible values of e given that the basic variables in the solution
of C remain the same.
(d) Find the solution to the following linear programme.
maximise -6x1 + 5x2 + 3x3 + 17x4.
subject to
2x1 + 2x2 + 5x3 + 6x4 < 38,
2x12x2 + 3x3 - 3x4≤ 49,
-2x1 + x₂ + 2x3+4x4≤ 8.
X1 ≥ 0, X₂ ≥ 0, x320, X4 ≥ 0.
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