2024知到网课 运筹学（四川师范大学）智慧树答案

第一章 单元测试

1、判断题：A basic feasible solution of an LP problem have one and only one related feasible basis.
A:对
B:错
正确答案:【错】

2、判断题：If the primal LP problem is unbounded, then the feasible region of dual problem must be empty.
A:对
B:错
正确答案:【对】

3、多选题：If the LP problem is solvable, then
A:The feasible region of this LP problem is nonempty
B:There exists an optimal basic feasible solution to this LP problem
C:There is a feasible regular solution of this LP problem
D:The value of the LP problem is finite
正确答案:【The feasible region of this LP problem is nonempty;There exists an optimal basic feasible solution to this LP problem;There is a feasible regular solution of this LP problem;The value of the LP problem is finite】

4、多选题：If the primal LP problem has optimal solutions, then
A:The dual problem is bounded
B:The feasible region of the dual problem is nonempty
C:The dual problem is non-degenerate
D:The dual problem has an optimal basic feasible solution
正确答案:【The dual problem is bounded;The feasible region of the dual problem is nonempty;The dual problem has an optimal basic feasible solution】

5、单选题：Which of the following assertions for the feasible region of a standard LP problem is incorrect?
A:The feasible region might have infinitely many vertices
B:The feasible region is convex
C:The feasible region might not have vertex
D:The feasible region might be unbounded
正确答案:【The feasible region might have infinitely many vertices】

第二章 单元测试

1、判断题：If the relaxed LP problem has feasible solution, then the related ILP problem has nonempty feasible region
A:对
B:错
正确答案:【错】

2、判断题：After adding the cutting plane, the new simplex table corresponds to a regular solution to the new LP problem
A:对
B:错
正确答案:【对】

3、判断题：In the branch-and-bound method, the bound is the value of cost function on a integer optimal solution to some relaxed sub-problem
A:对
B:错
正确答案:【对】

4、多选题：Which of the following assertions for the branch-and-bound method are correct?
A:If the value of current sub-problem is larger than the bound, the branch for this sub-problem should be cut off.
B:If the current sub-problem has integer optimal solution and the value is smaller than the bound, then the integer optimal solution is the solution to the original problem.
C:If the value of the sub-problem is smaller than the current bound and the optimal solution is not an integer solution, then this branch should be cut off.
D:If the corresponding relaxed LP problem has an integer optimal solution, then this solution is the optimal solution of ILP problem
正确答案:【If the value of current sub-problem is larger than the bound, the branch for this sub-problem should be cut off.;If the corresponding relaxed LP problem has an integer optimal solution, then this solution is the optimal solution of ILP problem】