midterm review IS
If the shadow price for a resource is 0 and 150 units of the resource are added, what happens to the optimal solution? It does not change. It increases by an unknown amount. It increases more than 0 but less than 150. It decreases by an unknown amount.
It does not change.
Level curves are used when solving LP models using the graphical method. To what part of the model do level curves relate? -Constraints -Objective function -Boundaries -Right hand sides
Objective function
The LHS value of a constraint represents the _________ of an associated resource by the decision variables. lower limit upper limit usage predicted value
usage
In an optimization problem, the mathematical symbols X1, X2, ..., Xn often represent the -objective. -constraints. -feasible region. -decision variables.
-decision variables.
The constraint for resource 1 is 5 X1 + 4 X2 ≥ 200. If X1 = 40 and X2 = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200? -80 -40 -0 -20
80
A manager has only 200 tons of plastic for his company. This is an example of a constraint. decision. objective. parameter
constraint.
Another term within Excel for decision variables is -decision cells. -variable cells. -objective cells. -constraint cells.
variable cells.
Better decision making using a modeling process is achieved due to the -visualization of the system being studied. -insight gained through the process. -timeliness of the results obtained. -interaction with the spreadsheet
-insight gained through the process.
A formulation has 10 variables and 4 constraints (not counting non-negativity). How many variables are basic? -4 -10 -14 -6
4
In the model Y = f(X1, X2), X1 is called a(n) -convoluted variable. -dependent variable. -confounded variable. -independent variable.
independent variable.
The desire to maximize profits is an example of a(n) parameter. constraint. objective. decision.
objective.
The shadow price of a nonbinding constraint is -positive. -negative. -zero. -indeterminate.
zero
In which of the following categories of modeling techniques are the specifications of the relationships between dependent and independent variables unknown or poorly defined -Predictive models -Prescriptive models -Open models -Descriptive models
Predictive models
If the constraint 2 X1 + 3 X2 ≥ 900 is binding, then the constraint 4 X1 + 6 X2 ≥ 600 is infeasible imiting. redundant. binding.
redundant.
A binding less than or equal to (≤) constraint in a maximization problem means -it is not a constraint that the level curve contacts. -that all of the resource represented by the constraint is consumed in the solution. -another constraint is limiting the solution. -the requirement for the constraint has been exceeded.
that all of the resource represented by the constraint is consumed in the solution.
How many decision variables are there in a transportation problem that has 5 supply points and 4 demand points? -4 -20 -5 -9
20
Consider the following formulation. The standard form of the second constraint is: MAX: 8 X1 + 4 X2 Subject to: 5 X1 + 5 X2 ≤ 20 6 X1 + 2 X2 ≥ 18 X1, X2 ≥ 0 6 X1 + 2 X2 + S2 = 18 5 X1 + 5 X2 = 20 6 X1 + 2 X2 = 18 6 X1 + 2 X2 - S2 = 18
6 X1 + 2 X2 - S2 = 18
A solvable problem must have -the best solution. -a feasible region that is not an empty set. -no more than two decision variables. -no more than two constraints
a feasible region that is not an empty set.
A heuristic solution is -guaranteed to produce an optimal solution. -a rule-of-thumb for making decisions. -used by Analytic Solver Platform (ASP) when the Guess button isused. -used by Analytic Solver Platform (ASP) if Standard GRG Nonlinear method is selected.
a rule-of-thumb for making decisions.
Models that are set up in an intuitively appealing, logical layout tend to be the most -modifiable. -reliable. -auditable. -organized
auditable.
The constraints of an LP model define the maximal region. feasible region. opportunity region. practical region.
feasible region.
The goal of the modeling approach to problem solving is to determine feasibility of decisions. determine a set of optimal decisions. help individuals make good decisions. ensure optimality of decisions.
help individuals make good decisions.
The first section of the Answer Report summarizes the original and final (optimal) value of the objective cell. decision variables. nonbinding constraints. binding constraints.
objective cell.
The notion that every problem is also an opportunity is reflected in the term -formulation. -simulation. -business opportunity. -probortunity.
probortunity.
Mathematical programming is an approach that involves determining how to allocate resources in such a way as to -predict the future. -minimize profits or maximize costs. -learn from past data. -maximize profits or minimize costs
-maximize profits or minimize costs
The simplex method of linear programming (LP) -does not convert all constraints to equalities. -evaluates all constraints for feasibility. -moves to a better and better corner point solution of the feasible region until no further objective function improvement can be achieved. -explicitly enumerates all corner points of the feasible region and selects the best objective function value.
-moves to a better and better corner point solution of the feasible region until no further objective function improvement can be achieved.
If results testing produces unsatisfactory results, -the problem-solving process requires new formulation and implementation. -testing should be repeated. -the solution algorithm should be checked. -minor adjustments should be made to the existing model.
-the problem-solving process requires new formulation and implementation.
The constraint for resource 1 is 5 X1 + 4 X2 ≤ 200. If X1 = 20, what is the maximum value for X2? -50 -20 -40 -25
25
A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X1, X2 and resource 1? 4 X1 + 3 X2 ≥ 150 4 X1 + 3 X2 ≤ 150 4 X1 ≤ 150 4 X1 + 3 X2 = 150
4 X1 + 3 X2 ≤ 150
In a decision-making framework, deserved success refers to a situation when which of the following occur? -Bad decision quality and bad outcome quality -Good decision quality and good outcome quality -Good decision quality and bad outcome quality -Bad decision quality and good outcome quality
Good decision quality and good outcome quality
Solutions to which of the following categories of modeling techniques indicate a course of action to the decision maker? Prescriptive models Descriptive models Predictive models Preventive models
Prescriptive models
The best models -replicate the characteristics of a component in isolation from the rest of the system. -replicate all aspects of the real-world object or decision. -accurately reflect relevant characteristics of the real-world object or decision. - are mathematical models
accurately reflect relevant characteristics of the real-world object or decision.
A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that -an error in formulation has been made. -the right-hand sides should be increased. -an alternate optimal solution exists. -the objective function needs new coefficients.
an alternate optimal solution exists.
Mathematical modeling approaches -are exhaustive. -are complementary. -cover the entire spectrum of decision support approaches. -are a subset of the total problem-solving process.
are a subset of the total problem-solving process.
Scaling problems include all of the following except that they -can cause Analytic Solver Platform to consider a linear problem as nonlinear. -can cause problems in accuracy of solutions returned. -are caused by small numbers and large numbers used in the same problem. -cannot prevent the computer from solving the problem at all
cannot prevent the computer from solving the problem at all
The essence of decision analysis is -choosing the best course of action among alternatives. -thinking ahead to avoid negative consequences. -finding the root cause of why something has gone wrong. -breaking down complex situations into manageable elements.
choosing the best course of action among alternatives.
A purely rational decision maker should -disregard the consequences of his or her choices. -allow emotions to influence the decision. -consistently select the same alternative, regardless of how the problem is framed. -always select optimal action.
consistently select the same alternative, regardless of how the problem is framed.
Limited resources are modeled in optimization problems as -alternatives. -an objective function. -decision variables. -constraints.
constraints
The sensitivity analysis provides information about all of the following except the impact of -a change to an objective function coefficient. -a change in a resource level. -adding simple upper or lower bounds on a decision variable. -constraints
constraints
Business opportunities can be viewed and formulated as -testing tools. -empirical models. -analytical models. -decision problems
decision problems
The objective function coefficients represent per-unit objective function contributions from one unit of the associated -decision variables. -data points. -feasible region. -constraints
decision variable
The second section of the Answer Report summarizes the original and final (optimal) values of the -objective cell. -binding constraints. -nonbinding constraints. -decision variables
decision variables
How much money an individual should withdraw each year from various retirement accounts is an example of a -decision. -constraint. -feasible region. -objective
decision.
The number of units to ship from Chicago to Memphis is an example of a(n) decision. parameter. constraint. objective
decision.
Alternate optimal solutions exist if the allowable increase or allowable decrease for the objective function coefficient for one or more variables is -less than 0. -slack. -binding. -equal to 0.
equal to 0
A production optimization problem has four decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact? -f(X1, X2, X3, X4) ≠ b1 -f(X1, X2, X3, X4) = b1 -f(X1, X2, X3, X4) ≥ b1 -f(X1, X2, X3, X4) ≤ b1
f(X1, X2, X3, X4) ≥ b1
Benefits of sensitivity analysis include all the following except that it -overcomes management skepticism of optimal solutions. -answers potential managerial questions regarding the solution to an LP problem. -fosters managerial acceptance of the optimal solution. -provides a better picture of how solutions change as model factors change.
fosters managerial acceptance of the optimal solution.
Chapter 1 discussed all of the following except -how to implement a problem formulation as a spreadsheet model. -how spreadsheet modeling and analysis fit into the problem-solving process. -how spreadsheet models of decision problems can be used to analyze the consequences of possible courses of action. -how models of decision problems differ in a number of important characteristics.
how to implement a problem formulation as a spreadsheet model.
The second step in formulating a linear programming problem is to -state the constraints as linear combinations of the decision variables. -state the objective function as a linear combination of the decision variables. -identify the decision variables. -understand the problem.
identify the decision variables.
Business analytics focuses on -identifying and leveraging business opportunities. -formulating analytical models. -using models to analyze problems. -testing and implementing results.
identifying and leveraging business opportunities.
Beneficial uses of the testing process include all of the following except -finding that some important assumption has been left out of the model. -giving no new insights into the nature of the problem. -double checking the validity of the model. -improving solutions after the implementation step
improving solutions after the implementation step
In a spreadsheet, input cells correspond conceptually to -dependent variables. -functions. -output cells. -independent variables
independent variables
If there is no way to simultaneously satisfy all the constraints in an LP model, the problem is said to be -open ended. -unbounded. -infeasible. -multi-optimal
infeasible
If an LP problem has an optimal solution with a finite objective function value, this solution will always occur at a point in the feasible region where two or more of the boundary lines of the constraints -are below the horizontal axis. -are perpendicular. -are parallel. -intersect
intersect
For an infeasible problem, the feasible region -has only one optimal solution. -has an infinite number of feasible solutions. -is an empty set. -is unbounded.
is an empty set.
A mathematical model is considered to be valid when -it replicates all aspects of the object or decision. -it has passed a validation test. -it accurately represents the relevant characteristics of the object or decision. -the left- and right-hand sides of expressions are equal
it accurately represents the relevant characteristics of the object or decision.
Retail companies try to find the -least costly method of transferring goods from warehouses to stores. -least profitable method of transferring goods from warehouses to stores. -largest number of goods to transfer from warehouses to stores. -most costly method of transferring goods from warehouses to stores.
least costly method of transferring goods from warehouses to stores
Linear programming problems have nonlinear objective functions and linear constraints. linear objective functions and nonlinear constraints. linear objective functions and linear constraints. nonlinear objective functions and nonlinear constraints.
linear objective functions and linear constraints.
A factor that plays a role in determining whether a good or bad outcome occurs is called intuition. certainty. luck. predictability.
luck.
How many basic variables are there in a linear programming model that has n variables and m constraints? n + m m n n − m
m
A facility produces two products and wants to maximize profit. The objective function to maximize is z = 350 X1 + 300 X2. The number 350 means that -one unit of product 1 contributes $350 to the objective function. -the problem has no constraints. -one unit of product 1 contributes $300 to the objective function. -the problem is unbounded.
one unit of product 1 contributes $350 to the objective function.
A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a(n) feasible solution. optimal solution. corner point solution. objective solution.
optimal solution.
Numeric constants should be -entered manually every time a model is solved. -placed in individual cells -embedded in formulas. -placed in separate workbooks
placed in individual cells
redundant constraint -is parallel to the level curve. -plays no role in determining the feasible region of the problem. -is added after the problem is already formulated. -can only increase the objective function value
plays no role in determining the feasible region of the problem
A situation when decision quality is bad and the resulting outcome quality is bad is referred to as pure luck. poetic justice. deserved success. bad luck.
poetic justice.
Identifying the real problems faced by the decision maker -requires insight, some imagination, time and a good bit of detective work. -will lead to developing the best model. -first requires a well-defined problem statement. -is not important since the decision maker has already defined the problem.
requires insight, some imagination, time and a good bit of detective work.
A mathematical programming application employed by a shipping company is most likely a manufacturing problem. routing and logistics problem. product mix problem. financial planning problem.
routing and logistics problem.
Consistently using a structured, model-based process to make decisions -is less effective than making decisions in a haphazard manner -always leads to well-deserved success in managerial decision making. -is evidence that luck plays an important role in decision making. -should produce good outcomes more frequently.
should produce good outcomes more frequently.
Solving LP problems in Excel requires -step-by-step formulation. -predictions about the future. -only copy and paste operations. -no additional add-ins.
step-by-step formulation.
The allowable decrease for a changing cell (decision variable) is -an indication of how many more units to produce to maximize profits. -the amount by which the constraint coefficient can decrease without changing the final optimal solution. -an indication of how much to charge to get the optimal solution. -the amount by which the objective function coefficient can decrease without changing the final optimal solution
the amount by which the constraint coefficient can decrease without changing the final optimal solution.
The allowable increase for a changing cell (decision variable) is -how much to charge to get the optimal solution. -the amount by which the constraint coefficient can increase without changing the optimal solution. -the amount by which the objective function coefficient can increase without changing the optimal solution. -how many more units to produce to maximize profit
the amount by which the objective function coefficient can increase without changing the optimal solution
The allowable decrease for a constraint is -the amount by which the constraint coefficient can increase without changing the final optimal value. -the amount by which the resource can decrease a given shadow price. -how much resource to use to get the optimal solution. -how many more units of resource to purchase to maximize profits
the amount by which the resource can decrease a given shadow price.
The allowable increase for a constraint is -how much resource to use to get the optimal solution. -how many more units of resource to purchase to maximize profits. -the amount by which the resource can increase a given shadow price. -the amount by which the constraint coefficient can increase without changing the final optimal value
the amount by which the resource can increase a given shadow price.
The reduced cost for a changing cell (decision variable) is -how many more units to product to maximize profits. -the per-unit profits minus the per-unit costs for that variable. -the amount by which the objective function value changes if the variable is increased by one unit. -equal to zero for variables at their optimal values
the per-unit profits minus the per-unit costs for that variable.
Spreadsheet modeling is an acquired skill because -the spreadsheet is free-form providing many modeling options. -spreadsheets are not very easy to use. -using Analytic Solver Platform requires lots of experience. -there is generally only one correct way to build a model.
the spreadsheet is free-form providing many modeling options
The intuitive approach to solving LP problems cannot be trusted because -most real-world problems are nonlinear. -real-world problems cannot be modeled mathematically. -there actually may be a better solution to the problem being modeled. -there are always errors in the LP formulations.
there actually may be a better solution to the problem being modeled
The first step in formulating an LP model is determining the number of variables. writing the constraints mathematically. understanding the problem to be modeled. determining the decision variables
understanding the problem to be modeled.
Which of the following is true of "What if?" analysis -"What if?" analysis is an efficient optimization technique. -"What if?" analysis is useful in creating a well-defined problem statement. -A well-designed spreadsheet facilitates "What if?" analysis. -It is not very useful when working with non-mathematical models.
-A well-designed spreadsheet facilitates "What if?" analysis.
Which of the following describes Data Envelopment Analysis (DEA) -DEA determines if a company is converting inputs to outputs as effectively as possible. -DEA compares how effective a company converts inputs to outputs compared to a benchmark composite of all companies. -DEA finds the most effective company among some set of companies. -DEA determines how effective a company converts inputs to outputs compared to other companies.
-DEA determines how effective a company converts inputs to outputs compared to other companies.
Which of the following is not true of a spider plot -It summarizes the optimal value for one input cell as individual changes are made to various output cells. -It is computationally expensive to generate for problems with many constraints and variables. -It is a graphical representation of multiple optimization runs. -It requires multiple runs of the problem
-It summarizes the optimal value for one input cell as individual changes are made to various output cells.
What is the significance of an absolute cell reference in Excel? -The cell reference will not change if the formula containing the reference is copied to another location -It is the only formula used to refer to a cell on another spreadsheet -The cell will always contain the absolute value of any number entered into it -The cell reference changes if the formula containing the reference is copied to another location
-The cell reference will not change if the formula containing the reference is copied to another location
Which of the following statements is true about different modeling techniques that are available to solve managerial decision problems? -The wrong choice of modeling technique is a common source of implementation difficulties. -The fundamental characteristics of the problem guide the selection of an appropriate modeling technique. -Managers should develop a strong preference and expertise in one technique to use when faced with problems. -Most problems faced by managers are fundamentally the sa
-The fundamental characteristics of the problem guide the selection of an appropriate modeling technique.
Which of the following statements is false concerning either of the Allowable Increase and Allowable Decrease columns in the Sensitivity Report? -The values provide a means to recognize when an alternate optimal solution exist. -The values equate the decision variable profit to the cost of resources expended. -The values give the range over which an objective function coefficient can change without changing the optimal solution. -The values give the range over which a shadow price is accurate
-The values equate the decision variable profit to the cost of resources expended.
When do alternate optimal solutions occur in LP models? -When a non-binding constraint is perpendicular to a level curve -Alternate optimal solutions indicate an infeasible condition -When a constraint is parallel to another constraint -When a binding constraint is parallel to a level curve
-When a binding constraint is parallel to a level curve
Anchoring effects occur in decision-making problems when -a seemingly trivial factor serves as a starting point for estimations. -a person in a position of authority exerts his or her opinion very forcefully. -organizations refuse to consider new alternatives. -decision makers are tied too closely to previous decisions.
-a seemingly trivial factor serves as a starting point for estimations.
Anchoring occurs when -an easy solution is obtained to a difficult problem. -a trivial factor is used as a starting point for estimations in a decision-making problem. -obtaining a solution is trivial. -a difficult factor is incorporated in a problem.
-a trivial factor is used as a starting point for estimations in a decision-making problem
The simplex method of linear programming (LP) -considers only the extreme points of the feasible region to achieve efficiency in solving LP problems. -explicitly enumerates all corner points of the feasible region and selects the best objective function value. -is not used in the Analytic Solver Platform software. -evaluates all constraints for feasibility.
-considers only the extreme points of the feasible region to achieve efficiency in solving LP problems.
Framing effects refer to -whether a software program can be used to obtain an optimal solution to a decision problem. -how structured the decision problem is. -how difficult a decision is. -how a decision maker views the alternatives in a decision problem
-how a decision maker views the alternatives in a decision problem
When a variable is basic, -it is present in the solution. -its value is equal to zero. -it may not be unique. -it is not present in the solution.
-it is present in the solution.
Finding a robust solution to an LP problem is -trivial. -beyond the scope of this class. -a guessing procedure. -one of the many useful features of the Analytic Solver Platform.
-one of the many useful features of the Analytic Solver Platform.
All of the following are CEO alternatives to start the OR/MS collaboration process except -require the OR/MS group to save their yearly salary in every study. -institute more participation from OR analysts. -use OR/MS personnel as consultants. -hire some OR/MS professionals and give them a problem to work
-require the OR/MS group to save their yearly salary in every study.
The solution to an LP problem is degenerate if the -shadow prices of any of the constraints have an allowable increase or allowable decrease of infinity. -right hand sides of any of the constraints have an allowable increase or allowable decrease of zero. -objective coefficients of any of the variables have an allowable increase or allowable decrease of zero. -shadow prices of any of the constraints have an allowable increase or allowable decrease of zero
-right hand sides of any of the constraints have an allowable increase or allowable decrease of zero.
Using Data Envelopment Analysis (DEA) for an inefficient unit, a more efficient composite unit can be found by -solving its DEA problem and examining those units whose final value is non-zero. -solving its DEA problem and using the positive resulting shadow prices as composite weights. -solving its DEA problem and using the resulting shadow prices as composite weights. -solving its DEA problem and retrieving the weights from the answer report.
-solving its DEA problem and using the resulting shadow prices as composite weights.
The third step in formulating a linear programming problem is to -state the objective function as a linear combination of the decision variables. -state the constraints as linear combinations of the decision variables. -understand the problem. -identify the decision variables
-state the objective function as a linear combination of the decision variables.
In spreadsheet modeling of a problem, -there is no relation between a mathematical equation and the spreadsheet. -there is a direct correspondence between a mathematical equation and the spreadsheet. -there is no direct correspondence between a mathematical equation and the spreadsheet. -there is very little correspondence between a mathematical equation and the spreadsheet.
-there is a direct correspondence between a mathematical equation and the spreadsheet.
A formulation has 20 variables and 8 constraints (not counting non-negativity). How many variables are nonbasic? 20 28 8 12
12
How many constraints are there in a transportation problem that has 5 supply points and 4 demand points? (Ignore the non-negativity constraints) 5 4 20 9
9
When performing sensitivity analysis, which of the following assumptions must apply? The non-negativity assumption can be relaxed. The X1 variable change is the most important. All other coefficients remain constant. Only right-hand side changes really mean anything
All other coefficients remain constant.
Which of the following types of effects arises when a seemingly trivial factor serves as a starting point for estimations in a decision-making problem? Anchoring Framing Underestimating Modeling
Anchoring
The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the Status Report. Cell Value Report. Slack Report. Answer Report.
Answer Report.
In a decision-making framework, poetic justice refers to a situation when which of the following occur Bad decision quality and bad outcome quality Good decision quality and good outcome quality Good decision quality and bad outcome quality Bad decision quality and good outcome quality
Bad decision quality and bad outcome quality
Which of the following fields of study uses computers, statistics, and mathematics to solve business problems? Accounting Business analytics Information systems Scientific management
Business analytics
Which type of spreadsheet cell represents the left hand sides (LHS) formulas in an LP model? Target or set cell Changing variable cell Constraint cell Constant cell
Constraint cell
Which of the following elements of a spreadsheet model can be empty cells? Data cells Constraints Objective function Decision variables
Decision variables
What are the three common elements of an optimization problem? -Decision variables, profit levels, and costs -Objectives, resources, and goals -Decisions, resource requirements, and a profit function -Decisions, constraints, and an objective
Decisions, constraints, and an objective
In which of the following categories of modeling techniques do the independent variables have unknown or uncertain values or coefficients? Prescriptive models Descriptive models Predictive models Probabilistic models
Descriptive models
Which of the following categories of modeling techniques addresses uncertainty in the values of the independent variables? -Scale models -Predictive models -Descriptive models -Prescriptive models
Descriptive models
Which of the following provide the most convenient, flexible, and useful way for business people to implement and analyze computer models? 3D printers Electronic spreadsheets Smartboards Graphing calculators
Electronic spreadsheets
Which of the following types of effects relates to how a decision maker views or perceives the alternatives in a decision problem Modeling Framing Anchoring Underestimating
Framing
In which step of the problem-solving process is the concept of "probortunity" introduced? Test results Identify problem Use model to analyze problem Formulate model
Identify problem
Which step of the problem-solving process is considered the most important? Analyze model Identify problem Implement solution Test results
Identify problem
Which of the following steps in the problem-solving process is most likely to incur resistance from people affected by the proposed solution? Formulate model Test results Use model to analyze problem Implement solution
Implement solution
Which of the following problem-solving steps is often considered the most difficult? Implement the solution. Test results. Analyze the model. Identify the problem.
Implement the solution.
Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value? Increase of 10 Increase of unknown amount Increase of 50 Decrease of 50
Increase of 50
Which of the following special conditions in an LP model represents potential errors in the mathematical formulation? Alternate optimum solutions and infeasibility Redundant constraints and unbounded solutions Alternate optimum solutions and redundant constraints Infeasibility and unbounded solutions
Infeasibility and unbounded solutions
Independent variables are represented as which type of cells in a spreadsheet model? Formula cells Dependent cells Output cells Input cells
Input cells
Implementing solutions to problems involves people and change. Which of the following is a suggested approach to effectively implement solutions? -Making decisions according to majority vote -More skillfully communicating management decisions -Centralizing decision-making authority to those who have specialized training in decision making -Involving anyone affected by the decision in all steps of the problem-solving process
Involving anyone affected by the decision in all steps of the problem-solving process
If the shadow price for a resource is 0 and 150 units of the resource are added, what happens to the objective function value? -It increases more than 0 but less than 150. -It does not change. -It increases by 150. -It increases by an unknown amount.
It does not change
Why is the graphical method of solving LP problems studied? -It helps develop an understanding of the linear programming strategy. -It provides better solutions than computerized methods. -It is faster than computerized methods. -Lines are easy to draw on paper.
It helps develop an understanding of the linear programming strategy.
If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value? It increases by an unknown amount. It increases by 110. It increases by 100. It decreases by 100
It increases by an unknown amount.
Which of the following statements is true of using models in problem solving and decision analysis? It is tied to the use of computers. It is a fairly new idea. It is required in order to find good solutions. It is something virtually everyone has done before.
It is something virtually everyone has done before.
Which of the following actions would expand the feasible region of an LP model? Multiplying each constraint by 2. Tightening the constraints. Adding an additional constraint. Loosening the constraints.
Loosening the constraints.
Which of the following is the type of model used throughout this textbook? Mental model Physical model Mathematical model
Mathematical model
Which of the following fields of business analytics finds the optimal method of using resources to achieve the objectives of a business? Mathematical programming Discriminant analysis Simulation Regression
Mathematical programming
Which of the following is most likely to be used when faced with the decision of how to arrange furniture in a room? Physical model Mathematical model Visual model Mental model
Mental model
Which type of spreadsheet cell represents the objective function in an LP model? Objective cell Constant cell Changing variable cell Constraint cell
Objective cell
Which of the following categories of modeling techniques involves determining the value of a dependent variable based on specific values of independent variables? Descriptive models. Prescriptive models. Biased models. Predictive models.
Predictive models.
Which of the following categories of modeling techniques includes optimization techniques? Capitalistic models Prescriptive models Predictive models Descriptive models
Prescriptive models
In the following expression, what is the dependent variable? PROFIT = REVENUE - EXPENSES
Profit
The simplex method uses which of the following values to determine if the objective function value can be improved? Shadow price Basic cost Target value Reduced cost
Reduced cost
Which of these most motivates a business to be concerned with efficient use of its resources? -Inefficient resource use increases business costs. -Resources are limited and valuable. -Efficient resources use means more free time. -Inefficient resource use means hiring more workers
Resources are limited and valuable.
Examining the effect of changes in the RHS values of constraints is part of the -Answer Report. -objective function. -feasible region. -Sensitivity Report.
Sensitivity Report.
To convert ≤ constraints into = constraints, the simplex method adds what type of variable to the constraint? Slack Dummy Spreading Redundant
Slack
Variables are termed independent when they satisfy which of the following? The function value depends upon their values. The decision maker has no control over them. The variable is described as an output of the spreadsheet model. The variables have no relationship to one another.
The function value depends upon their values.
For a minimization problem, if a decision variable's final value is 0, and its reduced cost is negative, which of the following is true? The variable has a non-negativity constraint. No feasible solution was found. Alternate optimal solutions exist. There is evidence of degeneracy
The variable has a non-negativity constraint.
What is the goal in optimization -To find the decision variable values that result in the best objective function and satisfy all constraints. -To find the values of the decision variables that use all available resources. -To find the values of the decision variables that satisfy all constraints. -To find the values of the decision variables that violate the least number of constraints
To find the decision variable values that result in the best objective function and satisfy all constraints.
In which step of the problem-solving process is the main focus to generate and evaluate alternatives? Formulate model Use model to analyze problem Test results Identify problem
Use model to analyze problem
Which type of spreadsheet cell represents the decision variables in an LP model? Constraint cell Target or set cell Variable cell Constant cell
Variable cell
A mathematical model uses mathematical relationships to represent a decision problem. a visual solution. the rate of change between two variables. predictions for the future.
a decision problem.
A valid model -produces an optimal solution. -produces a good solution. -produces a feasible solution. -accurately represents a decision problem being studied
accurately represents a decision problem being studied
If the allowable increase or allowable decrease for the objective function coefficient for one or more variables is equal to zero alternate optimal solutions exist. the solution is degenerate. the solution is infeasible. the shadow prices will be equal to zero.
alternate optimal solutions exist.
When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero, it indicates (in the absence of degeneracy) that -the problem is infeasible. -no optimal solution can be found. -alternate optimal solutions exist. -there is only one optimal solution.
alternate optimal solutions exist.
If a shadow price is positive for a maximization problem, a unit increase in the RHS value of the associated constraint results in -an infeasible solution. -an increase in the optimal objective function value. -no change in the optimal objective function value. -a decrease in the optimal objective function value.
an increase in the optimal objective function value.
Slack variables are always equal to zero. are usually negative. can be positive or negative. are always positive.
are always positive.
A situation when decision quality is good and the resulting outcome quality is bad is referred to as pure luck. bad luck. poetic justice. deserved success.
bad luck.
A solution to the system of equations using a set of basic variables is called a feasible solution. basic feasible solution. nonbasic feasible solution nonbasic solution.
basic feasible solution.
All of the following are reasons why someone would wish to use a spreadsheet model except to implement a computer model. because spreadsheets are convenient. to analyze decision alternatives. because spreadsheets lead to increased opportunities.
because spreadsheets lead to increased opportunities.
The slope of the level curve for the objective function value can be changed by doubling all the coefficients in the objective function. increasing the right-hand sides of constraints. changing a coefficient in the objective function. increasing the value of the decision variables.
changing a coefficient in the objective function.
In application, sensitivity analysis is a useful and practical way to -find an extreme corner point. -consider mathematical shortcomings. -determine the feasible region. -consider real-world uncertainties.
consider real-world uncertainties.
The symbols X1, Z1, Cat, and Dog are all examples of parameters. objectives. constraints. decision variables.
decision variables.
If constraints are added to an LP model, the feasible solution space will generally remain the same. decrease. increase. become more feasible
decrease.
In the model Y = f(X1, X2), Y is called a(n) -dependent variable. -independent variable. -confounded variable. -convoluted variable.
dependent variable
A situation when decision quality is good and the resulting outcome quality is good is referred to as dumb luck. poetic justice. deserved success. pure luck
deserved success.
A manager should consider how sensitive the model is to changes in all of the following except: differential coefficients. constraint coefficients. right-hand side values for constraints. objective function coefficients
differential coefficients.
A situation when decision quality is bad and the resulting outcome quality is good is referred to as deserved success. bad luck. poetic justice. dumb luck.
dumb luck.
The simplex method is computationally -inaccurate. -complex. -efficient. -simplified.
efficient.
The specification or description of the relationship between the dependent and independent variables is generally called a mathematical model. function. constraint. declaration.
function.
The simplex method works by first setting X1 at one-half of its maximum value. going directly to the optimal solution. identifying any basic feasible solution. choosing the largest value for X1.
identifying any basic feasible solution.
The ultimate goal of the problem identification step of the problem-solving process is -collecting lots of information. -convincing the decision maker the mess is really a problem that can be solved. -identifying the root problem(s) causing the mess. -helping the decision maker realize there is a problem.
identifying the root problem(s) causing the mess
Because they simplify reality, models are generally helpful in examining things that would be -quickly done in reality. -impossible to do in reality. -inexpensive to do in reality. -easily done in reality
impossible to do in reality.
The absolute value of the shadow price indicates the amount by which the objective function will be improved if the corresponding constraint is loosened. made worse if the corresponding constraint is loosened. improved if the corresponding constraint is unchanged. improved if the corresponding constraint is tightened.
improved if the corresponding constraint is loosened.
Virtually everyone who uses a spreadsheet today for model building and decision making -is in a position to influence decision makers. -is a practitioner of business analytics. -is a CPA. -possesses an advanced knowledge of mathematics and computer programming languages.
is a practitioner of business analytics.
A robust solution to an LP problem consists of all of the following except that it -has a reasonably good objective function value. -is sub-optimal. -is a solution in the interior of the feasible region. -is a solution on the boundary of the feasible region
is a solution on the boundary of the feasible region
If a problem has an infinite number of solutions, the objective function goes through exactly one corner point of the feasible region. cannot identify a feasible region. is infeasible. is parallel to one of the binding constraints.
is parallel to one of the binding constraints.
When building a model, it is often _____________ to analyze decision problems using a model than carrying out the decision in reality. more difficult less expensive more expensive a longer process
less expensive
The term "mathematics" is used to encompass not only the most familiar elements of math, such as algebra, but also profit and revenue calculations. calculus logic. expense calculations
logic.
Shadow prices represent the __________ of the resources in an LP problem. decision variables causal values marginal values slack variables
marginal values
A common objective in the product mix problem is maximizing production volume. maximizing profit. maximizing cost. minimizing production time.
maximizing profit.
When a solution is degenerate, the shadow prices and their ranges -are always valid and unique. -may be interpreted in the usual way but they may not be unique. -are always understated. -must be disregarded
may be interpreted in the usual way but they may not be unique.
When a solution is degenerate, the reduced costs for the changing cells may be set to any value the manager needs. may not be unique. are always equal to zero. are equal to infinity.
may not be unique.
Most individuals manage their individual retirement accounts (IRAs) so they maximize the amount of money they withdraw. leave all their money to the government. retire with a minimum amount of money. minimize the amount of taxes they must pay.
minimize the amount of taxes they must pay.
A common objective when manufacturing printed circuit boards (PCBs) is -minimizing the number of holes drilled. -maximizing the number of holes drilled. -minimizing the total distance the drill bit must be moved. -maximizing the number of drill bit changes.
minimizing the total distance the drill bit must be moved.
In mathematical linear programming formulations, the powers of all decision variables must be equal to 1. must be equal to 2. may contain squared terms. may contain cubic terms.
must be equal to 1.
Data Envelopment Analysis (DEA) is an LP-based methodology in which weighted sums of inputs and outputs are calculated and the -constraints ensure the sum of the weighted outputs is 1. -constraints capture the maximum effectiveness of each unit. -objective is to maximize every unit of output. -objective for each unit is to maximize the weighted sum of its outputs.
objective for each unit is to maximize the weighted sum of its outputs
Mathematical programming is referred to as satisficing. optimization. simulation. approximation.
optimization.
In modeling a problem, it is usually best to start by -formulating a cell in the spreadsheet that corresponds to the objective function. -entering all equations in a spreadsheet. -formulating the constraints. -organizing the data for the model on the spreadsheet.
organizing the data for the model on the spreadsheet.
A change in the right-hand side of a binding constraint may change all of the following except the slack values. the objective function value. other right-hand sides. the optimal value of the decision variables.
other right-hand sides.
The optimization technique that locates solutions in the interior of the feasible region is known as robust optimization. USET optimization. sensitivity analysis. sub-optimal optimization
robust optimization.
A constraint is binding if it is not redundant to another constraint in the model. redundant to another constraint in the model. satisfied as a strict equality in the optimal solution. not satisfied as a strict equality in the optimal solution
satisfied as a strict equality in the optimal solution.
When a manager considers the effect of changes in an LP model's coefficients, they are performing a sensitivity analysis. coefficient analysis. random analysis. qualitative analysis.
sensitivity analysis.
A change in the right-hand side of a constraint changes the objective function coefficients. the feasible region. the slope of the objective function. other right-hand sides.
the feasible region.
"Probortunity" is a decision support method. the first step in the problem-solving process. part of solution implementation. part of testing results.
the first step in the problem-solving process.
A binding greater than or equal to (≥) constraint in a minimization problem means that -the minimum requirement for the constraint has just been met. -the variable is up against an upper limit. -the shadow price for the constraint will be positive. -another constraint is limiting the solution.
the minimum requirement for the constraint has just been met
A linear formulation means that -at least one constraint must be linear. -only the objective function must be linear. -the objective function and all constraints must be linear. -no more than 50% of the constraints must be
the objective function and all constraints must be linear.
If the correct problem is not identified, the best that can be hoped for is -the right answer to the wrong question. -a descriptive model. -wasted time and effort. -useful experience in problem definition efforts.
the right answer to the wrong question.
When the objective function can increase without ever contacting a constraint, the LP model is said to be unbounded. open ended. multi-optimal. infeasible.
unbounded.
To be effective, a modeler must: collect the proper input data for the model. understand how modeling fits into the entire problem-solving process. be an effective presenter of results. apply the correct modeling technique.
understand how modeling fits into the entire problem-solving process.
The words "opportunity" and "problem" are complementary. used interchangeably. mutually exclusive. disjoint.
used interchangeably.
In order to be useful to a decision maker, decision problems need to be analyzed. valid. complicated. tested.
valid.
A road map is an example of a physical model. visual model. mathematical model. mental model.
visual model.
To illustrate how a complex system will be built, an engineer will likely use a mathematical model. mental model. visual model. physical model.
visual model.
The end result of the problem-identification step is a(n) implementation plan feasible solution to enact. well-defined statement of the problem. prediction for the related outcome.
well-defined statement of the problem.
Binding constraints have -surplus resources. -positive slack. -negative slack. -zero slack
zero slack
