运筹学（四川师范大学） 2024智慧树满分答案

惦肠龋付庞蛇铣渤比塘厢截渭

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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
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
答案: 对

3、多选题：
If the LP problem is solvable, then

A:The value of the LP problem is finite
B:There exists an optimal basic feasible solution to this LP problem
C:The feasible region of this LP problem is nonempty
D:There is a feasible regular solution of this LP problem
答案: The value of the LP problem is finite;There exists an optimal basic feasible solution to this LP problem;The feasible region of this LP problem is nonempty;There is a feasible regular solution of this LP problem

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 has an optimal basic feasible solution
D:The dual problem is non-degenerate
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 is convex
B:The feasible region might not have vertex
C:The feasible region might have infinitely many vertices
D:The feasible region might be unbounded
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
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
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
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 corresponding relaxed LP problem has an integer optimal solution, then this solution is the optimal solution of ILP problem
D: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.
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

5、多选题：
Which of the following assertions for the cutting plane method are correct?

A:If the relaxed problem has feasible solution, then the ILP problem has feasible solution
B:After adding the cutting plane, if the new relaxed problem is unsolvable then, the original ILP is unsolvable
C:After adding the cutting plane,one should using the dual simplex method to solve the new relaxed problem
D:In the procedure of solving ILP by cutting plane method,the feasible region of the relaxed LP problem will become smaller in each iteration.
答案: After adding the cutting plane, if the new relaxed problem is unsolvable then, the original ILP is unsolvable;After adding the cutting plane,one should using the dual simplex method to solve the new relaxed problem;In the procedure of solving ILP by cutting plane method,the feasible region of the relaxed LP problem will become smaller in each iteration.

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