Determine the set of all basic solutions of the following polyhedra and determine, for each basic solution, whether it is a vertex or not. (1.1) P {[x1, x2]T € R² : x1 – x2 < 1, 2x1 – 2x2 > -4, x1 > 0, –2x1 – x2 < -2}. К1.2) Р %—D {[x1, x2]T E R? : x1 > 0, x1 + x2 = -1, x2 > 0}. <1.3) Р — {x € R³ : x1+x2 – 2x3 < 5, x1 – x2+3x3 > -2, x1+3x2 – 7x3 = 0}.
Determine the set of all basic solutions of the following polyhedra and determine, for each basic solution, whether it is a vertex or not. (1.1) P {[x1, x2]T € R² : x1 – x2 < 1, 2x1 – 2x2 > -4, x1 > 0, –2x1 – x2 < -2}. К1.2) Р %—D {[x1, x2]T E R? : x1 > 0, x1 + x2 = -1, x2 > 0}. <1.3) Р — {x € R³ : x1+x2 – 2x3 < 5, x1 – x2+3x3 > -2, x1+3x2 – 7x3 = 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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![Determine the set of all basic solutions of the following polyhedra and determine, for each basic
solution, whether it is a vertex or not.
1T
(1.1) P =
{[x1, x2]" E R² : x1 – x2 < 1, 2x1 – 2x2 > -4, x1 > 0, –2x1 – x2 < -2}.
(1.2) P
{[x1, x2]" E R² : x1 > 0, x1 + x2 = -1, x2 > 0}.
(1.3) P
{x € R° : x1 + x2 – 2x3 < 5, xı – x2 + 3x3 > –2, x1 +3x2 – 7x3 = 0}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e09be7d-8a95-4622-860b-6e5f40e00af4%2Fc3b08c8e-5a0a-4ebb-b5cb-95119dcce37a%2F6jqud8g_processed.png&w=3840&q=75)
Transcribed Image Text:Determine the set of all basic solutions of the following polyhedra and determine, for each basic
solution, whether it is a vertex or not.
1T
(1.1) P =
{[x1, x2]" E R² : x1 – x2 < 1, 2x1 – 2x2 > -4, x1 > 0, –2x1 – x2 < -2}.
(1.2) P
{[x1, x2]" E R² : x1 > 0, x1 + x2 = -1, x2 > 0}.
(1.3) P
{x € R° : x1 + x2 – 2x3 < 5, xı – x2 + 3x3 > –2, x1 +3x2 – 7x3 = 0}.
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