BMGT332- Final Multiple Choice

Which of the following optimization tools is prepackaged with Excel?

Solver

What happens to the optimal solution (decision variables) when the RHS of a binding constraint increases within the allowable increase?

Some values in the optimal solution increase and others decrease.

A nonlinear solver uses the initial decision variables to start the search and the result may depend on the starting values.

True

A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.

True

Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times.

True

For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model.

True

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

True

In a shortest path problem, there is a unit supply at the origin and a unit demand at the destination.

True

In an assignment problem all supply and demand values are equal to one.

True

In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer.

True

In the maximal flow problem, one arc is added from the destination to the origin to formulate the problem as an LP model.

True

It is common in computer simulations to estimate the mean of some distribution by the average of the simulated observations. The usual practice is then to accompany this estimate with a confidence interval, which indicates the accuracy of the estimate.

True

LINDO is a specialized mathematical package that can solve large optimization problems.

True

Modeling efforts should be directed towards the goal of communications, reliability, auditability and modifiability.

True

Monte Carlo is a technique for selecting numbers randomly from a probability distribution.

True

Nonlinear programming algorithms occasionally have difficulty distinguishing between local optima and the global optimum.

True

One of the primary advantages of simulation models is that they enable managers to answer what-if questions about changes in systems without actually changing the systems themselves.

True

The terms in the objective function or constraints are additive.

True

A decision tree is a diagram consisting of

branches representing decision alternatives

Both linear and nonlinear programming models are examples of:

constrained optimization models

The _______________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.

expected value

In a transshipment problem, items may be transported

from one transshipment point to another, from destination to destination, directly from sources to destinations

The deterministic (non-simulation) approach, using best guesses for the uncertain inputs, is:

generally not the appropriate model

Unlike optimization models, simulation provides:

insights

Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.

parallel

The Lagrange multiplier reflects the appropriate change in the objective function for a unit change in the _______ of the constraint equation.

right-hand side

People who forgo a high expected value to avoid a disaster with a low probability are:

risk averters

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

sometimes, optimal

What happens to the feasible region when one of the coefficients in the objective function increases beyond the allowable increase?

the feasible region stays unchanged

The appropriate criterion is dependent on

the risk personality of the decision maker

In the linear programming formulation of a network flow problem,

there is one variable per arc, the total flow in and out of a node is constrained by the supply or demand at the node, and there is one constraint per node

Manual simulation is limited because of the amount of real time required to simulate even one trial.

true

If we change the RHS of a constraint beyond the allowable increase or decrease, the shadow price

will change

Decision variables cannot be multiplied by each other in the objective function of a nonlinear program.

False

If there are no feasible solutions to a linear programming model, then the best course of action for a manager is to choose a solution that violates the least number of constraints.

False

In the shortest path problem, one arc is added between the origin and destination to formulate the problem as an LP model.

False

Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3.

False

Multiple optimal solutions occur when constraints are parallel to each other.

False

Nonlinear programming has the same format as linear programming, however either the objective function or the constraints (but not both) are nonlinear functions.

False

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

False

The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin.

False

There is always exactly one optimal solution point to a linear program.

False

When solving a nonlinear program, the message "Solver found a solution. All constraints and optimality conditions are satisfied." means that a global optimal solution has been found for the problem.

False

When working with nonlinear optimization, there is no benefit in linearizing non-linear relationships that can be linearized.

False

What solving method is most generally used to solve nonlinear programs in Excel Solver?

GRG Nonlinear

Which of the following are assumptions or requirements of the transportation problem?

Goods are the same, regardless of source.

Which of the following is not a goal of spreadsheet design

Immutability

Determine the worst payoff for each alternative and choosing the alternative with the best worst is called:

Maximin

Decision variables: -Measure the objective function -Measure how much or how many items to produce, purchase, hire, etc. -Always exist for each constraint -Measure the values of each constraint

Measure how much or how many items to produce, purchase, hire, etc.

What of the following situations does not require the LP problem to be revised?

Multiple optimal solutionsWhat characteristic best describes a degenerate solution?

In the Solver window, the cell that contains the objective function is referred as

Objective Cell

Shadow price of a non-binding constraint is always __

0

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:

1

Identify the LHS (left hand side) of the following constraint: 2 X1 + 5 X2 >= 100

2 X1 + 5 X2

What characteristic best describes a degenerate solution?

A solution where an anomaly takes place

Which of the following statements is not true: -An infeasible solution violates all constraints. -A feasible solution point does not have to lie on the boundary of the feasible solution. -A feasible solution satisfies all constraints. -An optimal solution satisfies all constraints.

An infeasible solution violates all constraints.

What statement best describes the shadow price?

The shadow price is the change in the objective function per unit increase in the RHS of a constraint

What happens to the optimal solution (decision variables) when one of the coefficients in the objective function increases within the allowable increase?

The values in the optimal solution do not change.

A minimum spanning tree problem cannot be solved as an LP problem, but is solved easily using a simple manual algorithm.

True

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

True

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

The feasible solution area contains infinite solutions to the linear program.

True

The first step in formulating a linear programming model is to define the decision variables.

True

The graphical solution approach is limited to LP problems with just two decision variables; while appropriate computer software can solve almost any LP problem easily.

True

The highest point on each peak of a surface can be considered a local optimum, but the highest point among all of the peaks is the only global optimum.

True

The objective function is a linear relationship reflecting the objective of an operation.

True

The risk profile is an effective tool for breaking an expected monetary value into its component parts: possible outcomes and their chances.

True

What is the term used by Solver to describe decision variables?

Variable Cell

Is it possible to recognize that a problem has multiple optimal solutions by examining the Sensitivity Report?

Yes. The allowable decrease or increase of a decision variable is zero AND the allowable decrease or increase for all constraints is greater than 0.

Each different set of values obtained for the uncertain quantities in a simulation model can considered to be:

a scenario

For a maximization integer LP problem, the optimal objective value of the relaxed ILP is

an upper bound on the objective value of the ILP.

A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model.

assignment

In spreadsheet design, the ability to trace the steps followed to generate the different outputs from the model in order to understand the model and verify results is referred as

audibility

The expected value of perfect information:

is the minimum expected opportunity loss

The minimax regret criterion:

minimizes the maximum regret

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected.

must also

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

mutually exclusive