Chapter 2

Alternative optimal solutions occur when there is no feasible solution to the problem.

F

A redundant constraint results in a. no change in the optimal solution(s) b. an unbounded solution c. no feasible solution d. alternative optimal solutions

A

Which of the following special cases does not require reformulation of the problem in order to obtain a solution? a. alternate optimality b. infeasibility c. unboundedness d. each case requires a reformulation.

A

. Slack a. is the difference between the left and right sides of a constraint. b. is the amount by which the left side of a ≤ constraint is smaller than the right side. c. is the amount by which the left side of a ≥ constraint is larger than the right side. d. exists for each variable in a linear programming problem.

B

. Which of the following is a valid objective function for a linear programming problem? a. Max 5xy b. Min 4x + 3y + (2/3)z c. Max 5x2 + 6y2 d. Min (x1 + x2)/x3

B

A constraint that does not affect the feasible region is a a. non-negativity constraint. b. redundant constraint. c. standard constraint. d. slack constraint.

B

The improvement in the value of the objective function per unit increase in a right-hand side is the a. sensitivity value. b. dual price. c. constraint coefficient. d. slack value.

B

To find the optimal solution to a linear programming problem using the graphical method a. find the feasible point that is the farthest away from the origin. b. find the feasible point that is at the highest location. c. find the feasible point that is closest to the origin. d. None of the alternatives is correct.

D

. It is possible to have exactly two optimal solutions to a linear programming problem.

F

An infeasible problem is one in which the objective function can be increased to infinity.

F

The constraint 2x1 − x2 = 0 passes through the point (200,100).

F

Which of the following statements is NOT true? a. A feasible solution satisfies all constraints. b. An optimal solution satisfies all constraints. c. An infeasible solution violates all constraints. d. A feasible solution point does not have to lie on the boundary of the feasible region.

C

The three assumptions necessary for a linear programming model to be appropriate include all of the following except a. proportionality b. additivity c. divisibility d. normality

D

A range of optimality is applicable only if the other coefficient remains at its original value.

T

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables

T

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

T

The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50)

T

The standard form of a linear programming problem will have the same solution as the original problem.

T

. If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation? a. 300x1 + 125x2 > 4,000 b. 300x1 + 125x2 < 4,000 c. 425(x1 + x2) < 4,000 d. 300x1 + 125x2 = 4,000

b

In what part(s) of a linear programming formulation would the decision variables be stated? a. objective function and the left-hand side of each constraint b. objective function and the right-hand side of each constraint c. the left-hand side of each constraint only d. the objective function only

A

. A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a. a standard variable b. a slack variable c. a surplus variable d. a non-negative variable

B

. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is a. at least 1. b. 0. c. an infinite number. d. at least 2.

B

As long as the slope of the objective function stays between the slopes of the binding constraints a. the value of the objective function won't change. b. there will be alternative optimal solutions. c. the values of the dual variables won't change. d. there will be no slack in the solution.

C

Because surplus variables represent the amount by which the solution exceeds a minimum target, they are given positive coefficients in the objective function.

F

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative.

F

Decision variables a. tell how much or how many of something to produce, invest, purchase, hire, etc. b. represent the values of the constraints. c. measure the objective function. d. must exist for each constraint.

A

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called a. optimal. b. feasible. c. infeasible. d. semi-feasible.

C

All linear programming problems have all of the following properties EXCEPT a. a linear objective function that is to be maximized or minimized. b. a set of linear constraints. c. alternative optimal solutions. d. variables that are all restricted to nonnegative values.

C

The maximization or minimization of a quantity is the a. goal of management science. b. decision for decision analysis. c. constraint of operations research. d. objective of linear programming.

D

A linear programming problem can be both unbounded and infeasible.

F

A redundant constraint is a binding constraint

F

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

F

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

F

Only binding constraints form the shape (boundaries) of the feasible region

F

. The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.

T

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem

T

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

T

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in a. standard form. b. bounded form. c. feasible form. d. alternative form.

A

All of the following statements about a redundant constraint are correct EXCEPT a. A redundant constraint does not affect the optimal solution. b. A redundant constraint does not affect the feasible region. c. Recognizing a redundant constraint is easy with the graphical solution method. d. At the optimal solution, a redundant constraint will have zero slack.

D

In a feasible problem, an equal-to constraint cannot be nonbinding.

T