Consider the following linear program in standard form min{x1 – 2x2 + x3 – 2x4 : x1 + x2 + 2x3 + x4 = 4; -x1 – 2x2 + x3 + x4 = 2; x> 0} and the vertices (a) âî = [0,0, 2, 0]" . (b) âêt = [1,0, 0, 3]", (c) & = [0,2/3,0, 10/3]T. You can assume that the coefficient matrix A has full row rank. For each vertex, decide whether the vertex is optimal or not, and whether it is degenerate or not.
Consider the following linear program in standard form min{x1 – 2x2 + x3 – 2x4 : x1 + x2 + 2x3 + x4 = 4; -x1 – 2x2 + x3 + x4 = 2; x> 0} and the vertices (a) âî = [0,0, 2, 0]" . (b) âêt = [1,0, 0, 3]", (c) & = [0,2/3,0, 10/3]T. You can assume that the coefficient matrix A has full row rank. For each vertex, decide whether the vertex is optimal or not, and whether it is degenerate or not.
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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![Consider the following linear program in standard form
min{x1 – 2x2 + x3
2x4 : x1 + x2 + 2x3 + x4=
4; -x1 – 2x2 + x3 + x4 = 2; x > 0}
|
and the vertices
(a) â = [0,0, 2, 0]".
(b) ât = [1,0, 0, 3]",
(c) & = [0,2/3,0, 10/3]".
You can assume that the coefficient matrix A has full row rank. For each vertex, decide
whether the vertex is optimal or not, and whether it is degenerate or not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa290310a-dd9c-431f-9c5c-6815758e2d5d%2F5ede3c47-cfdc-45fe-a98e-3e42fc390d71%2Fqq04bsb_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following linear program in standard form
min{x1 – 2x2 + x3
2x4 : x1 + x2 + 2x3 + x4=
4; -x1 – 2x2 + x3 + x4 = 2; x > 0}
|
and the vertices
(a) â = [0,0, 2, 0]".
(b) ât = [1,0, 0, 3]",
(c) & = [0,2/3,0, 10/3]".
You can assume that the coefficient matrix A has full row rank. For each vertex, decide
whether the vertex is optimal or not, and whether it is degenerate or not.
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