1. In a model, $x_1 \ge 0$ and integer, $x_2 \ge 0$, and $x_3 = 0, 1$. Which solution would not be feasible?
a. $x_1 = 5, x_2 = 3, x_3 = 0$
b. $x_1 = 4, x_2 = 0.389, x_3 = 1$
c. $x_1 = 2, x_2 = 3, x_3 = 0.578$
d. $x_1 = 0, x_2 = 8, x_3 = 0$
2. Rounded solutions to linear programs must be evaluated for
a. feasibility and optimality.
b. sensitivity and duality.
c. relaxation and boundedness.
d. each of the above is true.
3. To perform sensitivity analysis involving an integer linear program, it is recommended to
a. use the dual prices very cautiously.
b. make multiple computer runs.
c. use the same approach as you would for a linear program.
d. use LP relaxation.
4. Let $x_1$ and $x_2$ be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer
below indicates that project 2 can be done only if project 1 is done?
a. $x_1 + x_2 = 1$
b. $x_1 + x_2 = 2$
c. $x_1 - x_2 \le 0$
d. $x_1 - x_2 \ge 0$
5. If the optimal solution to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.
a. True
b. False
6. Slack and surplus variables are not useful in integer linear programs.
a. True
b. False
7. Assuming $W_1, W_2$, and $W_3$ are 0-1 integer variables, the constraint $W_1 + W_2 + W_3 \le 1$ is often called a
a. multiple-choice constraint.
b. k out of n alternatives constraint.
c. mutually exclusive constraint.
d. co-requisite constraint.
8. Let $x_1, x_2$ and $x_3$ be 0 - 1 variables whose values indicate whether the projects are not done or are done. Which answer below
indicates that at least two of the projects must be done?
a. $x_1 + x_2 + x_3 \ge 2$
b. $x_1 + x_2 + x_3 \le 2$
c. $x_1 + x_2 + x_3 = 2$
d. $x_1 - x_2 = 0$
9. Let $x_1$ and $x_2$ be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer
below indicates that project 2 cannot be done if project 1 is done?
a. $x_1 + x_2 \le 1$
b. $x_1 + x_2 = 2$
c. $x_1 - x_2 \le 0$
d. $x_1 - x_2 \ge 0$
10. Binary variables can be used to model multiple-choice and mutually exclusive constraints.
a. True
b. False
