Exercise 5.2. Do not use MATLAB for this question. Consider the constraints 1 < 2rı + x2 < 4, 0 0. (a) Verify that the point r1 = r2 = 0 is not feasible. (b) Formulate a phase-1 LP with a single artificial variable. Define the phase-1 problem in such a way that you know an initial vertex for the phase-1 constraints in which 21 = x2 = 0. (c) Solve the phase-1 problem of part (b) using the simplex method for problems in all- inequality form. Give the value of the artificial variable at each iteration. (d) Use your phase-1 solution to define a feasible point for the original constraints. Is your solution a vertex for phase 2? Justify your answer.
Exercise 5.2. Do not use MATLAB for this question. Consider the constraints 1 < 2rı + x2 < 4, 0 0. (a) Verify that the point r1 = r2 = 0 is not feasible. (b) Formulate a phase-1 LP with a single artificial variable. Define the phase-1 problem in such a way that you know an initial vertex for the phase-1 constraints in which 21 = x2 = 0. (c) Solve the phase-1 problem of part (b) using the simplex method for problems in all- inequality form. Give the value of the artificial variable at each iteration. (d) Use your phase-1 solution to define a feasible point for the original constraints. Is your solution a vertex for phase 2? Justify your answer.
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:Exercise 5.2. Do not use MATLAB for this question. Consider the constraints
1< 2r1 + x2 < 4, 0< x1< 2, x2 > 0.
(a) Verify that the point a1 = x2 = 0 is not feasible.
(b) Formulate a phase-1 LP with a single artificial variable. Define the phase-1 problem
in such a way that you know an initial vertex for the phase-1 constraints in which
x1 = x2 = 0.
(c) Solve the phase-1 problem of part (b) using the simplex method for problems in all-
inequality form. Give the value of the artificial variable at each iteration.
(d) Use your phase-1 solution to define a feasible point for the original constraints. Is your
solution a vertex for phase 2? Justify your answer.
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