101 ch7

A multiple choice constraint involves selecting k out of n alternatives, where k ≥ 2.

False

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

False

If Project 5 must be completed before Project 6, the constraint would be x5 − x6 ≤ 0.

False

If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution

False

Slack and surplus variables are not useful in integer linear programs.

False

The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.

False

he constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.

False

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

True

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

True

If the optimal solution to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.

True

If x1 + x2 ≤ 500y1 and y1 is 0 - 1, then if y1 is 0, x1 and x2 will be 0.

True

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

True

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

True

Most practical applications of integer linear programming involve only 0 -1 integer variables.

True

Multiple choice constraints involve binary variables.

True

Some linear programming problems have a special structure that guarantees the variables will have integer values.

True

The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.

True

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

True

Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done? a. x1 + x2 + x3 ≥ 2 b. x1 + x2 + x3 ≤ 2 c. x1 + x2 + x3 = 2 d. x1 − x2 = 0

a

Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a a. multiple-choice constraint. b. mutually exclusive constraint. c. k out of n alternatives constraint. d. corequisite constraint.

b

Modeling a fixed cost problem as an integer linear program requires a. adding the fixed costs to the corresponding variable costs in the objective function. b. using 0-1 variables. c. using multiple-choice constraints. d. using LP relaxation.

b

The graph of a problem that requires x1 and x2 to be integer has a feasible region a. the same as its LP relaxation. b. of dots. c. of horizontal stripes. d. of vertical stripes.

b

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

False

Integer linear programs are harder to solve than linear programs.

True

The classic assignment problem can be modeled as a 0-1 integer program.

True

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

True

Most practical applications of integer linear programming involve a. only 0-1 integer variables and not ordinary integer variables. b. mostly ordinary integer variables and a small number of 0-1 integer variables. c. only ordinary integer variables. d. a near equal number of ordinary integer variables and 0-1 integer variables.

a

Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. each of these choices are true.

a

The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost.

a

The solution to the LP Relaxation of a maximization integer linear program provides a. an upper bound for the value of the objective function. b. a lower bound for the value of the objective function. c. an upper bound for the value of the decision variables d. a lower bound for the value of the decision variables

a

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables? a. supply chain design b. bank location c. capital budgeting d. product design and market share optimization

a

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.

b

Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be appropriate b. using 0-1 variables for modeling flexibility c. increased ease of solution d. provision for solution procedures for transportation and assignment problems

b

In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible? a. x1 = 5, x2 = 3, x3 = 0 b. x1 = 4, x2 = .389, x3 = 1 c. x1 = 2, x2 = 3, x3 = .578 d. x1 = 0, x2 = 8, x3 = 0

c

In an all-integer linear program, a. all objective function coefficients must be integer. b. all right-hand side values must be integer. c. all variables must be integer. d. all objective function coefficients and right-hand side values must be integer.

c

Rounding the solution of an LP Relaxation to the nearest integer values provides a. a feasible but not necessarily optimal integer solution. b. an integer solution that is optimal. c. an integer solution that might be neither feasible nor optimal. d. an infeasible solution.

c

Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation and should be disregarded. d. is most useful for 0 - 1 models.

c

If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a a. multiple-choice constraint. b. k out of n alternatives constraint. c. mutually exclusive constraint. d. corequisite constraint.

d

Let x1 and x2 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. x1 + x2 = 1 b. x1 + x2 = 2 c. x1 − x2 ≤ 0 d. x1 − x2 ≥ 0

d