Chapter 5 AGEC 3413

33) ________ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

28) In a(n) ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

59) If a maximization linear programming problem consists 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 feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never

A) always

66) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

A) multiple-choice

52) In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

A) total

83) In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already

B) can sometimes

60) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

B) mutually exclusive

56) If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible.

B) sometimes optimal and feasible.

67) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

C) conditional

69) For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down

C) down

51) In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

C) mixed

57) 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.

D) an enumeration method.

55) Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous

D) continuous

68) If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

D) corequisite

82) In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also

D) must also

58) If a maximization linear programming problem consists 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

D) sometimes, optimal

4) In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

TRUE

36) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a(n) ________ constraint.

conditional

31) A(n) ________ integer model allows for the possibility that some decision variables are not integers.

mixed

32) In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a(n) ________ constraint.

multiple-choice

35) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a(n) ________ constraint.

multiple-choice

37) Rounding a noninteger solution ________ to the nearest integer value will likely result in an infeasible solution.

up

39) In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________.

x1 = x2

54) Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value.

A) 0 or 1 only.

53) In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

B) 0-1

84) In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above

B) 1.

50) Types of integer programming models are: A) total. B) 0-1. C) mixed. D) total, 0-1, and mixed

D) total, 0-1, and mixed

10) In a mixed integer model, the solution values of the decision variables are 0 or 1.

FALSE

11) The branch and bound solution method cannot be applied to 0-1 integer programming problems.

FALSE

13) In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

FALSE

16) In Excel, a binary constraint in cell A1 is created using the =BIN($A$1) formula.

FALSE

21) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint.

FALSE

22) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

FALSE

23) If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

FALSE

26) A mixed integer program has only integers as a solution; they are simply mixed, as opposed to an integer program where they are specific to the decision variables.

FALSE

6) The management scientist's fiancé informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint.

FALSE

7) In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

FALSE

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

FALSE

1) The three types of integer programming models are total, 0-1, and mixed.

TRUE

12) In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

TRUE

14) The divisibility assumption is violated by integer programming.

TRUE

15) One type of constraint in an integer program is a multiple-choice constraint.

TRUE

17) Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

TRUE

18) A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

TRUE

19) The feasible region in an integer programming graph is composed of a lattice of points.

TRUE

2) In a total integer model, all decision variables have integer solution values.

TRUE

20) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

TRUE

24) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

TRUE

25) Integer constraints are entered in the inequality dialog box within Excel's Solver routine.

TRUE

3) In a 0-1 integer model, the solution values of the decision variables are 0 or 1.

TRUE

5) The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

TRUE

8) The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several unsold half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

TRUE

29) The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions.

branch and bound

30) "It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a(n) ________ constraint."

contingency or mutually exclusive

27) Rounding a noninteger solution ________ to the nearest integer guarantees a feasible, but perhaps suboptimal solution to an integer programming situation.

down

34) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a(n) ________ constraint.

mutually exclusive

38) In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________.

x1 + x2 = 1