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If a variable in a linear program is defined as nonpositive (e.g. x₁ ≤ 0), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x₁ : = -x₁ ≥ 0). If the solution to the Phase I LP has objective function value z = 0, then the original LP is infeasible. For binary variables x and y, "x is not equal to y" can be modeled by the constraint x = y - 1. The feasible region of an integer program is a subset of the feasible region of its LP relaxation. If an optimal solution for the LP relaxation is integer-valued, then the LP relax- ation and the IP have the same optimal objective function value. edge. A minimum spanning tree of a network will always include the shortest/least cost For binary variable x and continuous variable y, the statement "If x = y = 0" can be modeled by the constraint y ≤ M(1 − x) for arbitrarily large constant M. 1, then

If a variable in a linear program is defined as nonpositive (e.g. x₁ ≤ 0), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x₁ : = -x₁ ≥ 0). If the solution to the Phase I LP has objective function value z = 0, then the original LP is infeasible. For binary variables x and y, "x is not equal to y" can be modeled by the constraint x = y - 1. The feasible region of an integer program is a subset of the feasible region of its LP relaxation. If an optimal solution for the LP relaxation is integer-valued, then the LP relax- ation and the IP have the same optimal objective function value. edge. A minimum spanning tree of a network will always include the shortest/least cost For binary variable x and continuous variable y, the statement "If x = y = 0" can be modeled by the constraint y ≤ M(1 − x) for arbitrarily large constant M. 1, then

Advanced Engineering Mathematics
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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If a variable in a linear program is defined as nonpositive (e.g. x₁ ≤ 0), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x₁ = −x₁ ≥ 0). If the solution to the Phase I LP has objective function value z = 0, then the original LP is infeasible. For binary variables x and y, “x is not equal to y" can be modeled by the constraint x = y - 1. The feasible region of an integer program is a subset of the feasible region of its LP relaxation. If an optimal solution for the LP relaxation is integer-valued, then the LP relax- ation and the IP have the same optimal objective function value. edge. A minimum spanning tree of a network will always include the shortest/least cost = For binary variable x and continuous variable y, the statement "If x y = 0" can be modeled by the constraint y ≤ M(1 − x) for arbitrarily large constant M. 1, then
Transcribed Image Text:If a variable in a linear program is defined as nonpositive (e.g. x₁ ≤ 0), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x₁ = −x₁ ≥ 0). If the solution to the Phase I LP has objective function value z = 0, then the original LP is infeasible. For binary variables x and y, “x is not equal to y" can be modeled by the constraint x = y - 1. The feasible region of an integer program is a subset of the feasible region of its LP relaxation. If an optimal solution for the LP relaxation is integer-valued, then the LP relax- ation and the IP have the same optimal objective function value. edge. A minimum spanning tree of a network will always include the shortest/least cost = For binary variable x and continuous variable y, the statement "If x y = 0" can be modeled by the constraint y ≤ M(1 − x) for arbitrarily large constant M. 1, then
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