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(a) Solve the following linear programme using Simplex algorithm. Show the intermediate steps in the form of either the tableau or the dictionary. For each intermediate tableau/dictionary, identify the corresponding basic feasible solution. Maximise ₁ + 37₂ subject to ₁ + 1₂ ≤ 6 - 11 +21₂ ≤8 I1, I2 20

(a) Solve the following linear programme using Simplex algorithm. Show the intermediate steps in the form of either the tableau or the dictionary. For each intermediate tableau/dictionary, identify the corresponding basic feasible solution. Maximise ₁ + 37₂ subject to ₁ + 1₂ ≤ 6 - 11 +21₂ ≤8 I1, I2 20

Advanced Engineering Mathematics
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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Q2: (a) Solve the following linear programme using Simplex algorithm. Show the intermediate steps in the form of either the tableau or the dictionary. For each intermediate tableau/dictionary, identify the corresponding basic feasible solution. Maximise x₁ + 3x2 subject to x₁ + x₂ ≤ 6 -1 +21₂ ≤8 I1, I2 ≥ 0 (b) What is meant by polynomial time complexity in the context of linear programmes? Comment on the computational complexity of Simplex algorithm, Ellipsoid algorithm and the interior point methods for solving a linear programme. Which of these is known to run in polynomial time and which of them are fast in practice? (c) (i) Write the dual of the following linear program: Maximise 5x + 2y subject to - x + y ≤3 x+y=4 2x+y 22 x, y ≥0 (ii) Explain what is the meaning of the sensitivity interval associated with the right-hand side term of a constraint. If the right-hand side term of a constraint changes, but without leaving its sensitivity interval, which of the following will remain unchanged (i) the composition of the basis, or (ii) the value of the basic variables, or (iii) the value of the objective function?
Transcribed Image Text:Q2: (a) Solve the following linear programme using Simplex algorithm. Show the intermediate steps in the form of either the tableau or the dictionary. For each intermediate tableau/dictionary, identify the corresponding basic feasible solution. Maximise x₁ + 3x2 subject to x₁ + x₂ ≤ 6 -1 +21₂ ≤8 I1, I2 ≥ 0 (b) What is meant by polynomial time complexity in the context of linear programmes? Comment on the computational complexity of Simplex algorithm, Ellipsoid algorithm and the interior point methods for solving a linear programme. Which of these is known to run in polynomial time and which of them are fast in practice? (c) (i) Write the dual of the following linear program: Maximise 5x + 2y subject to - x + y ≤3 x+y=4 2x+y 22 x, y ≥0 (ii) Explain what is the meaning of the sensitivity interval associated with the right-hand side term of a constraint. If the right-hand side term of a constraint changes, but without leaving its sensitivity interval, which of the following will remain unchanged (i) the composition of the basis, or (ii) the value of the basic variables, or (iii) the value of the objective function?
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