Question 6 (5 pts) Multiple choice questions (6.1) Which of the following algorithms can be used to solve IP? (a) Enumeration method; (b) Branch and bound method; (c) Cutting plan method: (d) Approximation method. (6.2) The linear system has no feasible solutions if and only if (a) the system is feasible; (b) the system is feasible; (c) the system is feasible; (d) the system is feasible. (6.3) Which of the following algorithms can find the optimal solution to some transportation problem? (a) Vogel's penalty algorithm; (6) Minimum cost method; ) Hungarian method; (d) Simplex method. (6.4) Label the following statements regarding the traveling salesman problem as true or false? @) A tour that passes each city precisely once is a TSP tour, (b) A TSP tour is a tour that passes each city precisely once before returning to its starting city; ) The TSP problem can be easily solved as a shortest path problem (d) The TSP problem is very hard to solve but a good approximation can be obtained easily under certain conditions. (6.5) Label the following statements about ILP and its relaxation as true or false. (a) The feasible region of the ILP is a subset of the feasible region of its LP relaxation: (b) A feasible solution to the ILP is a comer point of the feasible region of its LP relaxation; (c) If the objective function value at the optimal solution of the LP relaxation is integer, then the optimal solution of the LP relaxation is also optimal for the original ILP, (d) Given a feasible non-integer solution to the LP relaxation, we can obtain a feasible solution to the original ILP by rounding each variable to its nearest integer