DSCI Exam 1

Which of the following is not a property of linear programs? at least two separate feasible regions one or more constraints one objective function alternative courses of action

At least two separate feasible regions

An objective function is necessary in a maximization problem but is not required in a minimization problem.

False

Any linear programming problem can be solved using the graphical solution procedure.

False

In a linear program, the constraints must be linear, but the objective function may be nonlinear.

False

In some instances, an infeasible solution may be the optimum found by the corner point method.

False

One of the assumptions of LP is "simultaneity."

False

The existence of non-negativity constraints in a two-variable linear program implies that we are always working in the northwest quadrant of a graph.

False

The rationality assumption implies that solutions need not be in whole numbers (integers).

False

The term slack is associated with ≥ constraints.

False

How do you calculate the number of constraints in transportation problem?

Sources + Destinations

How do you calculate the number of variables in transportation problem?

Sources x Destinations

Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple solutions.

True

If the isoprofit line is not parallel to a constraint, then the solution must be unique.

True

One of the assumptions of LP is "proportionality."

True

The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming.

True

The solution to a linear programming problem must always lie on a constraint.

True

The term surplus is associated with ≥ constraints.

True

Which of the following is not a property of all linear programming problems? a computer program optimization of some objective alternate courses of action to choose from the presence of restrictions

a computer program

Which of the following is not a part of every linear programming problem formulation? a. a redundant constraint b. an objective function c. a set of constraints d. non-negativity constraints

a redundant constraint

If a linear program is unbounded, the problem probably has not been formulated correctly. Which of the following would most likely cause this? a. A constraint was inadvertently omitted. b. An unnecessary constraint was added to the problem. c. The objective function coefficients are too large. d. The objective function coefficients are too small.

a. A constraint was inadvertently omitted.

In an LP problem, at least one corner point must be an optimal solution if an optimal solution exists. a. True b. False

a. True

Linear programming can be used to select effective media mixes, allocate fixed or limited budgets across media, and maximize audience exposure. a. True b. False

a. True

If the feasible region gets larger due to a change in one of the constraints, the optimal value of the objective function a. must increase or remain the same for a maximization problem. b. must decrease or remain the same for a maximization problem. c. must increase or remain the same for a minimization problem. d. cannot change.

a. must increase or remain the same for a maximization problem.

A feasible solution to an LP problem a. must satisfy all of the problem's constraints simultaneously. b. need not satisfy all of the constraints, only some of them. c. must be a corner point of the feasible region. d. must give the maximum possible profit.

a. must satisfy all of the problem's constraints simultaneously.

If a nonredundant constraint is removed from an LP problem, then a. the feasible region will get larger. b. the feasible region will get smaller. c. the problem would become nonlinear. d. the problem would become infeasible.

a. the feasible region will get larger.

When alternate optimal solutions exist in an LP problem, then a. the objective function will be parallel to one of the constraints. b. one of the constraints will be redundant. c. two constraints will be parallel. d. the problem will also be unbounded.

a. the objective function will be parallel to one of the constraints.

In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has? a. a redundant constraint. b. alternate optimal solutions. c. an unbounded solution. d. an infeasible solution.

an unbounded solution.

The lines in a network are called

arcs

An assignment problem may be viewed as a transportation problem with a. a cost of $1 for all shipping routes. b. all supplies and demands equal to 1. c. only demand constraints. d. only supply constraints.

b. all supplies and demands equal to 1.

In LP, variables do not have to be integer valued and may take on any fractional value. This assumption is called a. proportionality. b. divisibility. c. additivity. d. certainty.

b. divisibility.

Using LP to maximize audience exposure in an advertising campaign is an example of the type of LP application known as a. marketing research. b. media selection. c. portfolio assessment. d. media budgeting. e. all of the above.

b. media selection.

In a typical shortest-route model, the objective is to a. minimize the number of nodes in the route. b. minimize the time or distance to get from one point to another. c. minimize the number of arcs in the route. d. travel through all nodes in the best way possible.

b. minimize the time or distance to get from one point to another.

Four cranes are being assigned to five construction jobs. One of the jobs will be delayed until one of the cranes becomes available after finishing the first job. An assignment model will be used. To allow specialized software to find a solution to this problem, a. nothing special must be done to this problem. b. one dummy crane must be used in the model. c. one dummy job must be used in the model. d. both a dummy job and a dummy crane must be used in the model.

b. one dummy crane must be used in the model.

In the optimal solution to a linear program, there are 20 units of slack for a constraint. From this, we know that a. the dual price for this constraint is 20. b. the dual price for this constraint is 0. c. this constraint must be redundant. d. the problem must be a maximization problem.

b. the dual price for this constraint is 0.

An LP problem has a bounded feasible region. If this problem has an equality constraint, then a. this must be a minimization problem. b. the feasible region must consist of a line segment. c. the problem must be degenerate. d. the problem must have more than one optimal solution.

b. the feasible region must consist of a line segment.

1.When using a graphical solution procedure, the region bounded by the set of constraints is called a. the solution. b. the feasible region. c. the infeasible region. d. maximum profit region. e. none of the above.

b. the feasible region.

A large city is planning for the Olympic Games, which will be coming in a few years. The transportation system is being evaluated to determine what expansion is needed to handle the large number of visitors to the games. Which of the following models would most likely help the city planners determine the capacity of the current system? a. the transportation model b. the maximal-flow model c. the shortest-route model d. the minimal-spanning tree model

b. the maximal-flow model

A company is considering opening one new production facility, and three locations are being considered. For this facility location problem, how many transportation models must be developed and solved? a. 1 b. 2 c. 3 d.4

c. 3

Which of the following would cause a change in the feasible region? a. Increasing an objective function coefficient in a maximization problem b. Adding a redundant constraint c. Changing the right-hand side of a non redundant constraint d. Increasing an objective function coefficient in minimization problem

c. Changing the right-hand side of a non redundant constraint

A linear program has been solved, and sensitivity analysis has been performed. The ranges for the objective function coefficients have been found. For the profit on X1, the upper bound is 80, the lower bound is 60, and the current value is 75. Which of the following must be true if the profit on this variable is lowered to 70 and the optimal solution is found? a. A new corner point will become optimal. b. The maximum possible total profit may increase. c. The values for all the decision variables will remain the same. d. All of the above are possible.

c. The values for all the decision variables will remain the same.

In solving a linear program, no feasible solution exists. To resolve this problem, we might a. add another variable. b. add another constraint. c. remove or relax a constraint. d. try a different computer program.

c. remove or relax a constraint.

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as a. the product mix problem. b. the investment banker problem. c. the portfolio selection problem. d. the Wall Street problem. e. none of the above.

c. the portfolio selection problem.

A graphical method should only be used to solve an LP problem when a. there are only two constraints. b. there are more than two constraints. c. there are only two variables. d. there are more than two variables.

c. there are only two variables.

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) ________ of the feasible region. interior point or extreme point interior point or center corner point or extreme point maximum point or minimum point

corner point or extreme point

If a transportation problem has 4 sources and 5 destinations, the linear program for this will have a. 4 variables and 5 constraints. b. 5 variables and 4 constraints. c. 9 variables and 20 constraints. d. 20 variables and 9 constraints.

d. 20 variables and 9 constraints.

The diet problem is a. also called the feed mix problem in agriculture. b. a special case of the ingredient mix problem. c. a special case of the blending problem. d. all of the above.

d. all of the above.

Which of the following does not represent a factor a manager might consider when employing LP for production scheduling? a. labor capacity b. space limitations c. product demand d. risk assessment e. inventory costs

d. risk assessment

The computing center of a large university is installing fiber-optic cables to link fifteen buildings on campus. Which of the following models could be used to determine the least amount of cable required to connect all the buildings? a. the transportation model b. the maximal-flow model c. the shortest-route model d. the minimal-spanning tree model

d. the minimal-spanning tree model

Which network model is used to determine how to connect all points of a network together while minimizing the total distance between them? a. the assignment model b. the maximal-flow model c. the shortest-route model d. the minimal-spanning tree model

d. the minimal-spanning tree model

When applying LP to diet problems, the objective function is usually designed to a. maximize profits from blends of nutrients. b. maximize ingredient blends. c. minimize production losses. d. maximize the number of products to be produced. e. minimize the costs of nutrient blends.

e. minimize the costs of nutrient blends.

The circles in the network are called (Sources/destinations)

nodes

Infeasibility in a linear programming problem occurs when? the feasible region is unbounded. a constraint is redundant. more than one solution is optimal. there is no solution that satisfies all the constraints given.

there is no solution that satisfies all the constraints given.