Let a and BE R. Consider the linear optimization model: min s.t. x1 + x2 αX1 + βα2 > 1 x1 ≥ 0,₂ € R. Write the linear programming dual of (Pa,ß). Call it (Da‚ß). (Pa‚ß)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter3: Functions And Graphs
Section3.3: Lines
Problem 43E
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Let a and B E R. Consider the linear optimization model:
(Pa,8)
min
s.t.
X1 + x₂
αX1 + βα2 >1
x1 ≥ 0, x₂ € R.
Write the linear programming dual of (Pa,ß). Call it (Da‚ß).
α,β
Transcribed Image Text:Let a and B E R. Consider the linear optimization model: (Pa,8) min s.t. X1 + x₂ αX1 + βα2 >1 x1 ≥ 0, x₂ € R. Write the linear programming dual of (Pa,ß). Call it (Da‚ß). α,β
determine all values of a and ß for which
(Da‚ß) is infeasible. What does that mean about (Pa‚ß)?
(Da‚ß) is feasible, but not unbounded. What does that mean about (Pa,ß)?
(Da‚ß) is unbounded. What does that mean about (Pa,p)?
(Pa,ß) has multiple optimal solutions. (You reasoning should use complementarity slackness relation-
ships between primal and dual optimal solutions.)
Transcribed Image Text:determine all values of a and ß for which (Da‚ß) is infeasible. What does that mean about (Pa‚ß)? (Da‚ß) is feasible, but not unbounded. What does that mean about (Pa,ß)? (Da‚ß) is unbounded. What does that mean about (Pa,p)? (Pa,ß) has multiple optimal solutions. (You reasoning should use complementarity slackness relation- ships between primal and dual optimal solutions.)
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