[2021] Leeds - COMP3910 Combinatorial Optimisation - Final Exam - Q1 LPs and ILPs
Question 1 (LPs and ILPs)
State a True/False answer for each statement in the table: [9 marks]
True or False?
1.1 Adding a constraint to a linear programming problem increases the size of the feasible region
1.2 If the right-hand side of a constraint is changed, the feasible region will not be affected and remains the same
1.3 If the objective function coefficients are changed, the current optimal solution always changes
1.4 If an ILP is feasible, then its LP relaxation is always feasible
1.5 If an ILP is infeasible, then its LP relaxation is always infeasible
1.6 If an ILP is unbounded, then its LP relaxation is always unbounded
1.7 If the LP relaxation is feasible, then the ILP is always feasible
1.8 If the LP relaxation is infeasible, then the ILP is always infeasible
1.9 An optimal solution to an ILP can always be obtained by rounding an optimal solution to its LP relaxation
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