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[2021] Leeds - COMP3910 Combinatorial Optimisation - Final Exam - Q1 LPs and ILPs

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Question 1 (LPs and ILPs) CourseNana.COM

State a True/False answer for each statement in the table: [9 marks] CourseNana.COM

True or False? CourseNana.COM

  CourseNana.COM

1.1 Adding a constraint to a linear programming problem increases the size of the feasible region CourseNana.COM

1.2 If the right-hand side of a constraint is changed, the feasible region will not be affected and remains the same CourseNana.COM

1.3 If the objective function coefficients are changed, the current optimal solution always changes CourseNana.COM

1.4 If an ILP is feasible, then its LP relaxation is always feasible CourseNana.COM

1.5 If an ILP is infeasible, then its LP relaxation is always infeasible CourseNana.COM

1.6 If an ILP is unbounded, then its LP relaxation is always unbounded CourseNana.COM

1.7 If the LP relaxation is feasible, then the ILP is always feasible CourseNana.COM

1.8 If the LP relaxation is infeasible, then the ILP is always infeasible CourseNana.COM

1.9 An optimal solution to an ILP can always be obtained by rounding an optimal solution to its LP relaxation CourseNana.COM

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