332 MC

In excel, the ____ function can be used to generate random numbers.

Rand()

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

True

An assignment problem is a special form of transportation problem where all supply and demand values are 1

True

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

True

If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change

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

True

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

True

Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints.

True

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

True

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

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

A decision tree is a diagram consisting of

branches representing decision alternatives.

Both linear and nonlinear programming models are examples of:

constrained optimization models

A ____ represents a limitation to achieving maximum profits due to limited resources

constraint

The difference between the assignment and the transportation problem is that:

each supply and demand value is 1 in the assignment problem.

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

expected value

A change in the value of an objective function coefficient will always change the value of the optimal solution

false

The flaw of averages refers to

how averages hide the uncertainty in outcomes and the risks associated with a decision

Which of the following is not a goal of spreadsheet design? -Auditability -Immutability -Reliability -Communication

immutability

In a ______ linear programming model, the solution values of the decision variables are whole numbers

integer

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

The appropriate criterion is dependent on

the risk personality of the decision maker

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.

False

A nonlinear solver ignores the initial decision variables.

False

A rounded down integers solution CANNOT result in a less than optimal solution to an integer programming problem

False

A shortest path problem cannot be solved as an LP problem, but is solved easily using a simple manual algorithm.

False

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 a maximal flow problem, there is a unit supply at the origin and a unit demand at the destination.

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

Sensitivity Analysis can be used to determine the effect on the solution for changing several parameters at once

False

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

False

The first step in formulating a linear programming model is to define the objective function.

False

The sensitivity range for an objective function coefficient is the range of values over which the profit does not change

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

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

Multiple Optimal Solutions

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

Mutually exclusive

The shadow price of a binding constraint can take the following values:

Non-Zero

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

Objective Cell

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

Parallel

In a transshipment problem, items may be transported

- directly from sources to destinations -rom destination to destination -from one transshipment point to another.

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

In the linear programming formulation of a network flow problem

1 - the total flow in and out of a node is constrained by the supply or demand at the node 2- there is one constraint per node 3 - there is one variable per arc

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.

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

Auditability

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 objective function value when the RHS of a non binding constraint increases within the allowable increase?

The objective value stays the same.

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.

Which of the following statements is/are true regarding the normal distribution?

There is a 95% chance that values will be within ± 2 standard deviations of the mean.

A long period of real time can be represented by a short period of simulated time.

True

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

True

Rounding a noninterger solution values up to the nearest int value can result in an infeasible solution to an integer programming problem

True

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

True

Sensitivity analysis can be used to determine the effect on the solution for changing one parameter at a time

True

Spreadsheet simulation modeling is quite similar to the other modeling applications in that it begins with input variables and then relates these with appropriate Excel® formulas to produce output variables of interest.

True

The appropriate criterion is dependent on the risk personality and philosophy of the decision maker

True

The built-in functions in Excel®, along with the RAND function, can be used to generate random numbers from many different types of probability distributions.

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

True

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

True

The sensitivity range for a constraint quantity value if the range over which the shadow price is valid

True

In order to determine the value of discrete demand in a simulation model using Excel, the ________ function is used to associate a specific value of demand with a random number.

VLOOKUP()

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

Variable Cell

In a 0-1 integer program, if one investment requires the adoption of another investment too, this would be written as

X1 <= X2

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.

Developing the cumulative probability distribution helps to determine random number ranges

`True

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

The expected value of perfect information:

is the minimum expected opportunity loss

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

maximin

Decision variables:

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

If we change the RHS of a non-binding constraint beyond the allowable increase or decrease, the optimal solution

might change

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