1. Which of the following is true of the relationship between the value of the optimal integer solution and the value of the optimal solution to the LP Relaxation?

a. For integer linear programs involving minimization, the value of the optimal solution to the LP Relaxation provides an upper bound on the value of the optimal integer solution.

b. For integer linear programs involving maximization, the value of the optimal solution to the LP Relaxation provides a lower bound on the value of the optimal integer solution.

c. For integer linear programs involving minimization, the value of the optimal solution to the LP Relaxation provides a lower bound on the value of the optimal integer solution.

d. For any linear program involving either minimization or maximization, the value of the optimal solution to the LP Relaxation provides an infeasible value for the optimal integer solution.

4. Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

a. x ≥ My

b. x ≤ My

c. Mx ≤ y

d. xy ≥ M

3. The importance of _____ for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.

a. objective function

b. decision variables

c. sensitivity analysis

d. optimization analysis

5. For a location problem, if the variables are defined as xi = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by _____ for i = 1, 2, ..., n number of outlet stores included in the problem.

a. Min(∑xi)

b. Max(∑xi)

c. Min(πxi)

d. Max(πxi)

7. The objective function for an optimization problem is: Max 5x – 3y, with one of the constraints being x, y ≥ 0 and y integer. x and y are the only decisions variables. This is an example of a(n) _____.

a. all-integer linear program

b. mixed-integer linear program

c. LP relaxation of the integer linear program

d. binary integer linear program

8. In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.

a. 5%

b. 0%

c. infinity

d. a value equal to the number of integer constraints

9. The part-worths for each of the attribute levels obtained from an initial customer survey and the subsequent regression analysis can be used to determine the:

a. customer utility value.

b. optimal solution for the regression analysis.

c. overall profit for the company.

d. overall sales achieved by the company.

10. In a production application involving a fixed cost and a variable cost, the use of _____ makes including the fixed cost possible in a production model.

a. location variables

b. noninteger constraints

c. objective function coefficients

d. binary variables

11. Pink, green, and black will be _____ of the color attribute.

a. levels

b. constraints

c. regression constants

d. utility values

12. The available size of the trousers will be a(n) _____ in an integer programming model for this problem.

a. binary variable

b. constrain

c. attribute

d. regression constant

13. According to the _____ constraint, the sum of two or more binary variables must be equal to one.

a. conditional

b. corequisite

c. multiple-choice

d. mutually exclusive

14. In a fixed-cost problem, choosing excessively large values for the maximum production quantity will result in:

a. all reasonable levels of production.

b. no production.

c. no solution at all.

d. possibly a slow solution procedure.

16. An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. What category does the objective fall under?

• Capital budgeting
• covering problem
• fixed-cost
• Product design and market share optimization problem

17. In a fixed-cost model, each fixed cost is associated with a binary variable and a specification of the:

a. upper bound for the corresponding production variable.

b. upper bound for each of the binary variable.

c. integer constraints involving the corresponding production variables.

d. objective function involving these binary variables only.

18. Which of the following is true about the sensitivity analysis for integer optimization problems?

a. Sensitivity reports are readily available for integer optimization problems similar to the linear programming problems.

b. Because of the discrete nature of the integer optimization, Excel Solver takes much more time to calculate objective function coefficient ranges, shadow prices, and right-hand-side ranges.

c. The sensitivity analysis is not important for integer problems.

d. To determine the sensitivity of the solution to changes in model inputs for integer optimization problems, the data must be changed and the problem must be re-solved.

20. Which of the following is true of rounding the solution to an integer?

a. It always produces the most optimal integer solution.

b. It never produces a feasible solution.

c. It does not affect the objective function.

d. It may or may not be feasible.