# MAT 540 Week 9 Quiz 5

1. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer.

a. total

b. 0 – 1

c. mixed

d. all of the above

2. In a total integer model, some solution values for decision variables are integer and others can be non-integer. TRUE/FALSE

3. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. TRUE/FALSE

4. If a maximization linear programming problem consist of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ______ result in a(n) _____ solution to the integer linear programming problem.

A) always, optimal

B) always, non-optimal

C) never, non-optimal

D) sometimes, optimal

E) never, optimal

5. The branch and bound method of solving linear integer programming problems is an enumeration method. TRUE/FALSE

6. In a mixed integer model, all decision variables have integer solution values.

TRUE/FALSE

7. For a maximization integer linear programming problem, feasible solution is ensured by rounding _______ non-integer solution values if all of the constraints are less-than -or equal- to type.

A) up and down

B) up

C) down

D) up or down

8. In a total integer model, all decision variables have integer solution values. TRUE/FALSE

9. The 3 types of integer programming models are total, 0 – 1, and mixed. TRUE/FALSE

10. The branch and bound method of solving linear integer programming problems is _______.

A) an integer method

B) a relaxation method

C) a graphical solution

D) an enumeration method

11. The linear programming relaxation contains the _______ and the original constraints of the integer programming problem, but drops all integer restrictions.

different variables

slack values

objective function

decision variables

surplus variables

12. The branch and bound method can only be used for maximization integer programming problems. TRUE/FALSE

13. The solution value (Z) to the linear programming relaxation of a minimization problem will always be less than or equal to the optimal solution value (Z) of the integer programming minimization problem TRUE/FALSE

14. The implicit enumeration method

A) generates an optimal integer solution when no new constraints can be added to the relaxed linear programming model

B) eliminates obviously infeasible solutions and evaluates the remaining solutions to determine which one is optimal

C) is used to solve a mixed integer linear programming model

D) cannot be used to solve linear programming models with multiple infeasible solutions

15.Types of integer programming models are _____________.

A) total

B) 0 – 1

C) mixed

D) all of the above

16. In a 0 – 1 integer model, the solution values of the decision variables are 0 or 1.

TRUE/FALSE

17. Which of the following is not an integer linear programming problem?

A) pure integer

B) mixed integer

C) 0-1integer

D) continuous

18. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. TRUE/FALSE

19. Rounding small values of decision variables to the nearest integer value causes _______ problems than rounding large values.

similar

more

fewer

none of the above

20. In using rounding of a linear programming model to obtain an integer solution, the solution is ___________.

always optimal and feasible

sometimes optimal and feasible

always optimal

always feasible

never optimal and feasible

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