BMGT332 Final Exam Multiple Choice
The sensitivity range for an objective function coefficient is the range of values over which the profit does not change. TRUE OR FALSE
FALSE
A long period of time can be represented by a short period of simulated time. TRUE OR FALSE
False
Decision variables cannot be multiplied by each other in the objective function of a nonlinear program. TRUE OR FALSE
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: True or False
False
In a maximal flow problem, there is a unit supply at the origin and a unit demand at the destination: True or False
False
In the shortest path problem, one arc is added between the origin and the destination to formulate the problem as an LP model: True or False
False
Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3: True or False
False
Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. TRUE OR FALSE
False
The branch and bound solution method cannot be applied to 0-1 integer programming problems. TRUE OR FALSE
False
The first step in formulating a linear programming model is to define the objective function: True or False
False
When working with nonlinear optimization, there is no benefit in linearizing non-linear relationships that can be linearized. TRUE OR FALSE
False
What solving method is most generally used to solve nonlinear programs in Excel Solver? a) LP Simplex b) GRG Nonlinear c) Simplex LP or GRG Nonlinear d) Evolutionary
GRG Nonlinear
In formulating a mixed integer programming problem, the constraints x1 + x2 <=500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1+x2 = 500 if y1 is: a) 0 b) none of these options c) 1 d) 0 or 1
1
If we are solving a 0-1 integer programming problem, the constraints x1 + x2 <= 1 is a __________ constraints. a) multiple-choice b) corequisite c) conditional d) mutually exclusive
Mutually exclusive
In the Solver window, the cell that contains the objective function is referred as a) variable cell b) objective cell c) target cell d) objective function
Objective cell
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. a) RAND () b) VLOOKUP() c) POISSON() d) INPUT()
RAND()
In excel, the ________ function can be used to generate a random number
Rand()
If we change the constrain quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change. TRUE OR FALSE
TRUE
Sensitivity analysis can be used to determine the effect on the solution for changing one parameter at a time. TRUE OR FALSE
TRUE
The sensitivity range for a constraint quantity is the range over which the shadow price is valid. TRUE OR FALSE.
TRUE
A minimum spanning tree problem can't be solved as an LP problem, but is solved easily using a simple manual algorithm: True or False
True
A payoff table is means of organizing a decision situation, including the payoffs from different decisions given the various states of nature. TRUE OR FALSE
True
An assignment problem is a special form of transportation problem where all supply and demand values equal 1. TRUE OR FALSE
True
Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times. TRUE OR FASLE
True
Developing the cumulative probability distribution helps to determine random number ranges. TRUE OR FALSE
True
For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model: True or False
True
In an assignment problem all supply and demand values are equal to one: true or false
True
In the shortest path problem, there is a unit supply at the origin and a unit demand at the destination: true or false
True
Manual simulation is limited because of the amount of real time to simulate even on trial. TRUE OR FALSE
True
Modeling efforts should be directed toward the goal of communications, reliability, auditability, and modifiability: True or False
True
Nonlinear programming algorithms occasionally have difficulty distinguishing between the local optima and the global optimum. TRUE OR FALSE
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 OR FALSE
True
Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. TRUE OR FALSE
True
The appropriate criterion is dependent on the risk personality and philosophy of the decision maker. TRUE OR FALSE
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 OR FALSE
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 or False
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 OR FALSE
True
The risk profile is an effective tool for breaking an expected monetary value into its component parts: possible outcomes and their chances. TRUE OR FALSE
True
The terms in the objective function or constraints are additive: True or False
True
What happens to the optimal solution (decision variables) when the RHS of a binding constraint increases within the allowable increase? a) some values in the optimal solution increase and others decrease b) the values in the optimal solution decrease c) the values in the optimal solution increase d) the values in the optimal solution do not change
a) some values in the optimal solution increase and others decrease
What is the method of the solving method used for linear optimization? a) CPLEX b) Simplex LP c) Linear Solve d) GRG Nonlinear
b) Simplex LP
What is the term used by Solver to describe decision variables? a) Objective cell b) Variable cell c) Constraint cells d) Decision cell
b) Variable cell
Decision Variables: a) measure the objective function b) measure how much or how many items to produce, purchase, hire, etc. c) always exist for each constraint d) measure the values of each constraint
b) measure how much or how many items to product, purchase, hire, etc.
A decision tree is a diagram consisting of a) branch angles that vary as likelihoods increase b) triangle probability nodes c) branches representing decision alternatives d) perfect information
branches representing decision alternatives
While of the following optimization tools is prepackaged with Excel? a) @Risk b) Lindo c) Solver d) None of these
c) Solver
Both of linear and nonlinear programming models are the examples of: a) simple tableaus b) goal programming models c) constrained optimization models d) constrained likelihood models
constrained optimization models
A ________________ represents a limitation to achieving maximum profits due to limited resources
constraints
Identify the LHS of the following constraint: 2X1 + 5X2 >= 100 a) >= b) 100 c) 2X1 d) 2X1 + 5X2
d) 2X1 + 5X2
What characteristic best describes a degenerate solution? a) a solution that is not unique b) an incorrect solution c) a solution that is not a corner point d) a solution where an anomaly takes place
d) a solution where an anomaly takes place
In a transshipment problem, items may be transported a) form one transshipment point to another b) from destination to destination c) directly from sources to destinations d) all of the options
d) all of the options
In linear programming formulation of a network flow problem, a) there is one variable per arc b) there is one constraint per node c) the total flow in and out of a node is constrained by the supply or demand at the node d) all options are correct
d) all options are correct
Multiple optimal solutions can occur when the objective function line is _______ to a constraint line. a) symmetrical b) vertical c) perpendicular d) parallel
d) parallel
The ____________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. a) expected value b) expected value of perfect information c) expected opportunity loss d) none of the given options
expected value
In a _________ programming model, the solution of the decision variables are whole numbers
integer
Which of the following statements is/are true regarding a simulation model? a) it makes decision-making easier b) it explicitly incorporates uncertainty in one or more input variables c) it does not require any best guesses d) all of these statements are true
it explicitly incorporates uncertainty in one or more input variables
The minimax regret criterion: a) maximizes the minimum regret b) minimizes the maximum regret c) maximizes the minimum payoff d) minimizes the maximum payoff
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 a) can also b) can never c) must also d) can sometimes
must also
The Lagrange multiplier reflects the appropriate change in the objective function for a unit change in the _____________ of the constraint equation. a) shadow price b) right-hand side c) objective function d) coefficient
right-hand side
People who forgo a high expected value to avoid a disaster with a low probability are: a) risk takers b) risk averters c) risk calculators d) risk predictors
risk averters
The appropriate criterion is dependent on a) the risk personality of the decision maker b) the number of decisions and chance events c) the magnitude of the payoffs d) none of the options
the risk personality of the decision maker
In a 0-1 integer program, if one investment requires the adoption of another investment too, this would be written as: ____________
x1<=x2
In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. TRUE OR FALSE
True
Monte Carlo is a technique for selecting numbers randomly from a probability distribution. TRUE OR FALSE
True
If we change the RHS of a non-binding constraint beyond the allowable increase or decrease, the optimal solution a) will not change b) will increase c) might change d) will decrease
c) might change
What happens to the feasible region when one of the coefficients in the objective function increases beyond the allowable increase? a) the feasible region gets smaller b) the feasible region gets bigger c) the feasible region changes, not possible to determine if bigger or smaller d) the feasible region stays unchanged
d) the feasible region stays unchanged
The ______________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence a) expected value b) expected value of perfect information c) expected opportunity loss d) none of the given options
expected value
The deterministic (non-simulation) approach, using best guesses for the uncertain inputs, is: a) better to used in complicated real world applications b) a good estimate of what the answer will be using a simulation approach c) generally not the appropriate model d) the preferred approach when there is correlation between input variables
generally not the appropriate model
The flaw of averages refers to a) the benefit of using averages on decision models b) the fact that the average is sensitive to outliers c) how averages hide the uncertainty in outcomes and the risks associated with a decision d) the difficulty of calculating averages of uncertain inputs
how averages hide the uncertainty in outcomes and the risks associated with a decision
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 _________ results in a(n) __________ solution to the integer a) never, non-optimal b) sometimes, optimal c) always, optimal d) always, non-optimal
sometimes, optimal
A rounded-down integer solution CANNOT result in a less than optimal solution to an integer programming problem. TRUE OR FALSE
FALSE
A change in the value of an objective function coefficient will always change the value of the optimal solution. TRUE OR FALSE
False
A nonlinear solver ignores the initial decision variables. TRUE OR FALSE
False
A shortest path problem cannot be solved as an LP problem, but it is solved easily using a simple manual algorithm: True or False
False
Nonlinear programming has the same format as linear programming, however either the objective function or the constraints (but not both) are nonlinear functions. TRUE OR FALSE
False
The optimal solution for a graphical linear programming problem is the corner point that is farthest from the origin: True or False
False
There is always exactly one optimal solution point to a linear programming: True or False
False
When solving a nonlinear program, the message "Solver found a solution. All constraints and optimally conditions are satisfied." means that a global optimal solution has been found for the problem. TRUE OR FALSE
False
The objective function always consists of either maximizing or minimizing some value: True or False
True
A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes, and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in: a) the same product mix, same total profit b) a different product mix, different total profit c) the same product mix, different total profit d) a different product mix, same total profit as before
a different product mix, different total profit
Each different set of values obtained for the uncertain quantities in a simulation model can be considered to be: a) the mean of the probability distribution b) a scenario c) a best guess d) all of these choices
a scenario
The feasible region of an ILP is (Mark all that correspond) a) convex b) a set of disconnected points c) a polygon d) continuous
a set of disconnected points
What of the following situations doesn't require the LP problem to be revised? a) multiple optimal solutions b) LP unboundedness c) Non-linear constraints d) LP infeasibility
a) Multiple optimal solutions
For a maximization integer LP problem, the optimal objective value of the relaxed ILP is a) an upper bound on the objective value of the ILP b) a lower bound on the objective value of the ILP c) a lower bound on the decision variables of the ILP d) an upper bound on the decision variables of the ILP
a) an upper bound on the objective value of the ILP
In a spreadsheet design, the ability to trace the steps followed to generate the different outputs form the model in order to understand the model and verify results is referred as a) auditability b) reliability c) verfication d) validation
a) auditability
Which of the following are assumptions or requirements of the transportation problem? a) goods are the same, regardless of source b) there must be multiple destinations c) there must be multiple sources d) there must be multiple routes between each sources and destination
a) goods are the same, regardless of source
Which of the following is not a goal of a spreadsheet design a) immutability b) communication c) reliability d) auditability
a) immutability
Determining the worst payoff for each alternative and choosing the alternative with the best worst is called: a) maximin b) minimin c) maximax d) minimax
a) maximin
The shadow price of a binding constraint can take the following values: a) less than 0 b) non-zero c) zero d) greater than 0
b) non-zero
What statement best describes the shadow price? a) the shadow price is the change in the objective function per unit increase in the RHS of a constraint b) the shadow price is the price of an asset in the parallel market c) the shadow price is the change in the RHS of a constraint per unit change in the objective function of an optimization problem d) the shadow price is the price of an additional unit of a scarce resource in an optimization problem
a) 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? a) the values in the optimal solution don't change b) Some values in the optimal solution increase and others decrease c) the value in the optimal solution increase d) the values in the optimal solution decrease
a) the values in the optimal solution don't change
The flaw of averages indicates that a) the average is not always a good description of the actual situation b) the function of the average is not always the same as the average of the function c) the average depends on your perspective d) all of the above e) none of the above
all of the above
Is it possible to recognize that a problem has multiple optimal solutions by examining the Sensitivity report? a) No. Solver reports only one solution and it is not possible to know if the problem has other optimal solution b) 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. c) Yes. The allowable decrease or increase of a constraint is 0 when there are multiple optimal solutions. D) Yes. The allowable decrease or increase of a decision variable is zero AND for a constraint as well.
b) 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.
The expected value of perfect information: a) is the difference between expected payoff and opportunity loss b) is the minimum expected opportunity loss c) is the difference between the expected value with perfect information and the minimum expected payoff d) is the maximum expected opportunity loss
is the difference between expected payoff and opportunity loss
