Consider the following two sets: S₁ = (x ER²: -2 ≤ x₁ + 2x₂ ≤ 4} U (x ER²: 0≤ 3x1-x2 ≤ 6) S₂ = (x ER²: x₁ + x₂ ≥ 3,2x₁ + x2 ≥ 4, x1 ≥ 0, x2 ≥ 0} For each of the above sets, answer the following questions (you can use well-drawn and accurate pictures) • Is it a convex set? Explain your answer. • Is it a polyhedron? Explain your answer. • If it is a polyhedron, find all the basic solutions and identify them as feasible and infeasible.
Consider the following two sets: S₁ = (x ER²: -2 ≤ x₁ + 2x₂ ≤ 4} U (x ER²: 0≤ 3x1-x2 ≤ 6) S₂ = (x ER²: x₁ + x₂ ≥ 3,2x₁ + x2 ≥ 4, x1 ≥ 0, x2 ≥ 0} For each of the above sets, answer the following questions (you can use well-drawn and accurate pictures) • Is it a convex set? Explain your answer. • Is it a polyhedron? Explain your answer. • If it is a polyhedron, find all the basic solutions and identify them as feasible and infeasible.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider the following two sets:
S₁ = {x ER² -2 ≤ x₁ + 2x₂ ≤ 4} U {x ER²: 0≤ 3x₁ - x2 ≤6)
S₂ = (x ER²: x₁ + x₂ ≥ 3,2x₁ + x2 ≥ 4, x₁ ≥ 0, x2 > 0}
x1
For each of the above sets, answer the following questions (you can use well-drawn and accurate pictures):
• Is it a convex set? Explain your answer.
• Is it a polyhedron? Explain your answer.
• If it is a polyhedron, find all the basic solutions and identify them as feasible and infeasible.
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