Prescriptive Analytics

The optimal solution to a NLP problem can occur at a(n) I.corner point. II.interior point.

c. I and II are true

Binary variables are useful for modeling

a. the fixed-charge problem

The transshipment nodes in the graphical representation of the transshipment problem:

a. have total demanded quantities expressed as positive numbers

One reason to use queuing models in business is

a. to trade-off the cost of providing service and the cost of customer dissatisfaction

Neural networks technique attempts to learn

a. what relationship exists between a set of input and output variables

Steps in the data mining process include the following (in sequence)

a.(identify opportunity), (collect data), (explore, understand and prepare data), (identify tasks and tools, (partition data), (build and evaluate models), (deploy models)

Which of the following formulas is a deviation-minimizing objective function for a goal programming problem?

a.M{ (D1- + D1+)

Which of the following is true regarding goal programming?

a.The objective function is not useful when comparing goal programming solutions. b. We can place upper bounds on any of the deviation variables. c. A preemptive goal program involves deviations with arbitrarily large weights. ALL OF THESE

Why would someone wish to use a spreadsheet model?

a.To implement a computer model. b. Because spreadsheets are convenient. c. To analyze decision alternatives. ALL OF THESE

Large sample size, n, is desirable because

b. upper and lower limits of the confidence interval for the true population mean are closer to one another

The standard prediction error is

b. used to construct confidence intervals for predicted values.

Solver can be used to estimate model parameters when the time series is stationary and additive seasonal effects are present.

True

Which of the following is the typical operating characteristic for average time a unit spends waiting for service?

b. Wq

When using the Regression tool in Excel the independent variable is entered as the

b. X-range.

A renege refers to

b. a customer who joins the queue but leaves before service is complete.

The LP relaxation of an ILP problem

b. always encompasses all the feasible integer solutions to the original ILP problem.

In solving the NLP problem, Solver found a degenerate model. This means that:

c. Solver is cycling and redundant constraints must be removed

What is the meaning of the t i term in this objective function for a goal programming problem? ​

c. The target value for goal i.

Logistic regression in XLMiner add-in can be used for ______ groups

2

A change in the right hand side of a constraint changes

c. the feasible region

The specification or description of the relationship between the dependent and independent variables is generally called

a function.

In a decision-making problem, anchoring effects occur when

a seemingly trivial factor serves as a starting point for estimations

As the number of replicates in a simulation increases the width of a confidence interval computed from the simulation results will

a. decrease.

For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

b. A lower bound.

The estimated value of Y 1 is given by

Y1=B0+B1X1

Expected regret is also called

b. EOL.

What is the formula for the exponential utility function U(x)?

d. 1 − e−x/R

In a queuing problem, Wq > W.

False

Goal programming (GP) is:

b. iterative

A course of action intended to solve a problem is called a(n)

alternative

Suppose that all observations belong to the same class. The entropy measure for this situation is equal to

c. 0

Prediction step in data mining is an option available in

d. XLMiner Excel add-in

A common objective when manufacturing printed circuit boards is

minimizing the total distance the drill bit must be moved

A redundant constraint is one which

plays no role in determining the feasible region of the problem

When the lines connecting the nodes in a network are arrows that indicate a direction, the arcs in the network are called directed arcs.

True

​ A problem in which all decision variables are restricted to assuming only integer values is called a pure IP programming problem.

True

​ The objective function coefficients represent per unit objective function contributions from one unit of the associated decision variables.

True

​ The second step in Goal Programming is defining the goals

True

​A simple linear regression model is of the form: Yi = β 0 + β 1 X1i + ε i

True

​Data mining is the process of finding and extracting useful information and insights from large data sets.

True

​The main difference between shadow prices and Lagrange multipliers involves the range of RHS values over which the shadow price or Lagrange multiplier remains valid

True

​The term "risk" also implies the potential for loss.

True

Rounding the LP relaxation solution up or down to the nearest integer may:

d. produce an infeasible solution

A mathematical model is considered to be "valid" when

it accurately represents the relevant characteristics of the object or decision.

A situation when decision quality is bad and the resulting outcome quality is bad is referred to as

poetic justice

The categories of modeling techniques presented in this book include all of the following except:

preventive models.

If results testing produces unsatisfactory results

the problem-solving process requires new formulation and implementation

To be effective, a modeler must

understand how modeling fits into the problem-solving process.

In order to be useful to a decision-maker, decision problems need to be

valid

Sensitivity analysis is useful in considering real-world uncertainties ​without resolving the entire formulation.

True

Shadow prices represent the marginal values of the resources in an LP problem,

True

The TREND( ) function can be used to calculate the estimated values for linear regression models.

True

The decision rules that assume that probabilities of occurrence can be assigned to the states of nature in a decision problem are called probabilistic methods.

True

The decisions in an optimization problem are often represented in a mathematical model by the symbols X1, X2, ..., Xn.

True

A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C?

20 A + 30 B ≥ 100

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X 1 = number of product 1 produced in each batch X 2 = number of product 2 produced in each batch MAX:150 X1 + 250 X2Subject to:2 X1 + 5 X2 ≤ 200 3 X1 + 7 X2 ≤ 175 X1, X2 ≥ 0

2750

In this text we use the term "mathematics" to encompass i.familiar elements of math such as algebra .ii.logic.

Both i and ii

Exhibit 3.3The following questions are based on this problem and accompanying Excel windows.Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit. LetX1 = Number of liters of product A in total blend delivered X2 = Number of liters of product B in total blend delivered MIN:7 X1 + 3 X2Subject to:X1 + X2 = 1.5 * 50 (Total liters of mix) X1 ≥ 0.48 * 1.5 * 50 (X1 minimum) X2 ≥ 0.5 * 50 (X2 minimum) .0.95 X1 + 0.78 X2 ≥ 0.85 * 1.5 * 50 (85% alcohol minimum) X1, X2 ≥ 0 ABCDE1 Jacks' Distillery 2 3 AB 4Liters to use Total Cost:5Unit cost:10.54.5 6 7Constraints: SuppliedRequirement8Total Liters11 759A required1 3610B required 1 251185% alcohol0.950.78 63.752 3 AB 4Liters to use Total Cost:5Unit cost:10.54.5 6 7Constraints: SuppliedRequirement8Total Liters11 759A required1 3610B required 1 251185% alcohol0.950.78 63.75

D8:D11

A residual is defined as the difference between the fitted value based on a model and a corresponding actual value.

False

A situation where cars arrive at an intersection can be modeled as an M/D/s queue with finite capacity.

False

Decision variables are sometimes referred to as problem parameters. ​

False

Examining the effect of changes ​in the RHS values of constraints is part of the answer report.

False

In a network flow problem, t he value +80 next to a node indicates that the number of units needs to decrease by 80.

False

Linear programming problems cannot have multiple objectives​

False

S easonality is a regular, repeating pattern in the data that takes longer than 1 year to complete.

False

Several techniques are available to help managers analyze risk. Three of the most common are best-case/worst-case analysis, what-if analysis, and simulation. Of these methods, what-if analysis the most powerful.

False

The expected monetary value decision rule selects the decision alternative with the largest expected regret.

False

Values of the binary integer variable are ​restricted to -1 or 1.

False

​ An extreme point of the feasible region can include negative values of coordinates.

False

​ In modeling a problem it is usually best to start by entering all equations in a spreadsheet.

False

​A given local optimal solution is also a global optimal solution to a NLP problem

False

​A problem in which some decision variables are restricted to assuming only integer values is called a 0-1 programming problem.

False

Implementing solutions to problems involves people and change. Which of the following is a suggested approach to effectively implement solutions?

Involve anyone affected by the decision in all steps of the problem-solving process

Which of the following statements is true of using models in problem solving and decision analysis?

It is something everyone has done before.

The memoryless property is also referred to as the ____ property.

Markov

In the following expression, which is (are) the dependent variable(s)? ​ PROFIT = REVENUE − EXPENSES

Profit

The Simplex method uses which of the following values to determine if the objective function value can be improved?

Reduced cost

Using Data Envelopment Analysis (DEA) for an inefficient unit, a more efficient composite unit can be found by

Solving its DEA problem and using the resulting shadow prices as composite weights.

The demand nodes in the graphical representation of the transshipment problem:

The demand nodes in the graphical representation of the transshipment problem:

In the face of uncertainty, some people react with paralysis, or they do exhaustive research to avoid making a decision.

True

A NLP problem can have nonlinear objective and a nonlinear constraints

True

An analyst can apply a process known as rolling back to a decision tree to determine the decision with the largest EMV.

True

If the number of arrivals in a given period of time follows a Poisson distribution with mean λ, the interarrival times follow an exponential probability distribution with mean 1/λ

True

Based on the following regression output, what is the equation of the regression line? Regression Statistics Multiple R 0.917214 R Square 0.841282 Adjusted R Square 0.821442 Standard Error 9.385572 Observations 10 ANOVA df SS MS F Significance F Regression 1 3735.3060 3735.30600 42.40379 0.000186 Residual 8 704.7117 88.08896 Total 9 4440.0170 Coefficients Standard Error t Stat P-value Lower 95% Intercept 31.623780 10.442970 3.028236 0.016353 7.542233 X Variable 1 1.131661 0.173786 6.511819 0.000186 0.730910

Y1= 31.62378 + 1.13661XII

The regression residuals are computed as

Yi-Yi... little triangle above the second Yi

In a model Y=f(x 1, x 2), Y is called:

a dependent variable.

The following questions use the information below.A decision maker is faced with two alternatives. The decision maker has determined that she is indifferent between the two alternatives when p = 0.45. Alternative 1:Receive $82,000 with certaintyAlternative 2:Receive $143,000 with probability p and lose $15,000 with probability (1 −p). Refer to Exhibit 14.7. What is the expected value of Alternative 2 for this decision maker?

a. $56,100

The right hand side value for the ending node in a shortest path problem has a value of

a. 1

If the arrival process is modeled as a Poisson random variable with arrival rate λ, then the average time between arrivals is

a. 1/λ

Refer to Exhibit 11.10. What are predicted sales for the fourth quarter of year 4?

a. 1460 ≤ predicted sales < 1465

Refer to Exhibit 11.8. What formula should be entered in cell E7 to compute the base level value for year 2 Quarter 1?

a. =$D$17*D7/G3+(1-$D$17)*(E6+F6)

If cell B2 contains the value for μ and cell A5 contains the value for T, what formula should go in cell B5 to compute the P(Service time) ≤ T for this exponential distribution?

a. =1-EXP(-$B$2*A5)

Which function is equivalent to =SUMPRODUCT(A1:A3,B1:B3)?

a. =A1*B1+A2*B2+A3*B3

An investor is developing a portfolio of stocks. She has identified 3 stocks to invest in. She wants to earn at least 5% return but with minimum risk. The problem data is given in the following Excel spreadsheet. What formula should be entered in cell G4 of the Excel spreadsheet? A B C D E > 1 > 2 Annual Return > 3 Year A B C > 4 1 3.98% 7.38% 8.76% > 5 2 −1.51% 10.45% 6.66% > 6 3 5.36% 5.15% 6.55% > 7 4 4.98% 5.51% −1.58% > 8 5 3.12% 6.93% 8.43% > 9 6 5.58% −4.32% 9.07% > 10 7 3.49% 9.78% 9.65% > 11 8 −2.37% 5.62% 8.96% > 12 9 5.92% 6.28% −7.10% > 13 10 5.69% 5.75% 10.96% > 14 > 15 Average 3.42% 5.85% 6.03% > ​ < F G H I J < 1 < 2 Covariance Matrix < 3 A B C < 4 A 0.00080 −0.00044 −0.00045 < 5 B −0.00044 0.00144 −0.00012 < 6 C −0.00045 −0.00012 0.00300 < 7 < 8 A B C Total < 9 Portfolio 36.8% 40.6% 22.6% 100.0% < 10 < 11 Expected Return 5.00% < 12 Required Return 5.00% < 13 < 14 Portfolio Variance 0.000274

a. =COVAR(B4:B13,$B$4:$B$13)

Refer to Exhibit 14.8. What formula should go in cell G11 and get copied to G12:G13 of the Price worksheet to compute the Consistency Measure?

a. =MMULT(C4:E4,$F$11:$F$13)/F11

Exhibit 3.1The following questions are based on this problem and accompanying Excel windows.Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced. LetX1 = Number of Beds to produce X2 = Number of Desks to produce The LP model for the problem is MAX:30 X1 + 40 X2Subject to:6 X1 + 4 X2 ≤ 36 (carpentry) 4 X1 + 8 X2 ≤ 40 (varnishing) X2 ≤ 8 (demand for desks) X1, X2 ≥ 0 ABCDE1 Jones Furniture 2 3 BedsDesks 4Number to make: Total Profit:5Unit profit:3040 6 7Constraints: UsedAvailable8Carpentry64 369Varnishing48 4010Desk demand 1 8 Refer to Exhibit 3.1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?

a. =SUMPRODUCT(B8:C8,$B$4:$C$4)

Refer to Exhibit 11.1. What Excel function will compute the mean squared error in cell C18 of the spreadsheet?

a. =SUMXMY2(B7:B14,C7:C14)/COUNT(C7:C14)

Which of the following best describes a random variable?

a. A spreadsheet input cell containing a random number generator. b. The outcome of a simulation model. c. Any variable whose value cannot be predicted with certainty. ALL OF THESE

Refer to Exhibit 11.10. How is a quadratic term added to the problem if we want to develop a quadratic trend model?

a. Add a column containing Time2.

Refer to Exhibit 14.1. What decision should be made according to the maximin decision rule?

a. C

Goal programming solution feedback indicates that the d 4 + level of 50 should not be exceeded in future solution iterations. How should you modify your goal constraint ​ 40 X1 + 20 X2 + d4− + d4+ = 300 ​ to accommodate this requirement?

a. Do not modify the constraint, add a constraint d4+ ≤ 50.

The concept of an upper bound in IP is associated with:

a. LP relaxation of a maximization problem

If a service system has a constant service time, Poisson arrival rates and 2 servers its Kendall notation is

a. M/D/2

A doctor's office only has 8 chairs. The doctor's service times and customer inter-arrival times are exponentially distributed. What type of system is it?

a. M/M/1 with Finite Queue

Which of the following are potential pitfalls of using a non-zero integer tolerance factor in the Analytic Solver Platform?

a. No assurance the returned solution is optimal.

How should one determine which RNGs to employ in a spreadsheet simulation model?

a. The distributions selected should represent the underlying pool of values expected to occur.

Why might a forecaster calculate MSE values on just the most recent data in the time-series data set?

a. The forecaster might be interested in how well the forecasting method performs on the more recent data. b. Because the most recent data may be a better predictor of future values. c. Because the resulting forecasting function might fit the older data better that the more recent data. ALL OF THESE

Which of the following do not help determine the magnitude of risk in a decision-making problem?

a. The level of management interest in the problem.

Every nonprobabilistic method has a weakness for decision making. Which of the following is incorrect regarding a method and its weakness?

a. The maximax method ignores potentially large losses. b. The maximin method ignores potentially large payoffs. c. The minimax regret method can lead to inconsistent decisions. All of these are correct.

Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is big and positive. This means that

a. The observation is likely to be classified correctly to group 2

Why would a manager be interested in analyzing risk?

a. To determine a distribution of outcomes.

Which of the following probability distributions are associated with continuous outcomes?

a. Triangular

How are states of nature assigned probabilities?

a. Use historical data. b. Use best judgement. c. Use interview results. All of these.

A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected?

a. X1 + X2 + X3 + X4 ≤ 2

In solving the NLP problem, Solver produced a message "Solver cannot improve the current solution. All constraints are satisfied." This means that Solver found:

a. a degenerate model

For a network with n nodes, a spanning tree is

a. a set of (n-1) arcs that connects all nodes and contains no loops

In a what-if analysis the decision maker

a. changes the values of the uncertain input variables to see what happens to the performance measure being studied

The terms b 0 and b 1 are referred to as

a. estimated population parameters.

The terms b 0 and b 1 are

a. estimated population parameters. b. estimated intercept and slope values, respectively. c. random variables. ALL OF THESE

Simulation is used to

a. find distribution information for the dependent variable(s).

A common queue discipline used in practice is

a. first-in-first-out

The setup cost incurred in preparing a machine to produce a batch of product is an example of a

a. fixed charge.

The supply nodes in the graphical representation of the transshipment problem:

a. have total available quantities expressed as negative numbers

The expected monetary value criterion (EMV) is the decision-making approach used

a. in decision-making under risk

The number of constraints in network flow problems is determined by the number of

a. nodes.

Worst case analysis is a(n) ____ view of the problem.

a. pessimistic

What method is used to generate observations from a distribution?

a. random number generator

Suppose that two variables are found to be significantly correlated. A researcher may

a. remove one variable from the data set

A soft constraint

a. represents a target a decision-maker would like to achieve

In hierarchical clustering, the measure of similarity between clusters is/are

a. single linkage b. average linkage c. average group linkage all of the above

In hierarchical clustering, the measure of similarity between clusters is/are

a. single linkage b. complete linkage c. Ward's method ALL OF THESE

A constraint which represents a target value for a problem is called a

a. soft constraint

Mixed IP formulation requires that:

a. some decision variables must be integer

The idea that the total flow into a node must be consumed at a node and the remainder must flow out of a node is referred to as:

a. the conservation of flow principle

If using the regression tool for two-group discriminant analysis, in the regression dialog box, the Input X-Range entry corresponds to

a. the independent variable values.

Scaling problems

a.can cause Analytic Solver Platform to consider a linear problem as nonlinear. b. can cause problems in accuracy of solutions returned. c. are caused by small numbers and large numbers used in the same problem. all of these.

Two of the effects associated with decision problems are:

anchoring and framing.

Decision models are applicable when

b. there are multiple alternatives

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)?

b. .80 X13 + .95 X23 − X35 − X36 − X37 = 0

Joe's Copy Center has 10 copiers. They break down at a rate of 0.02 copiers per hour and are sent to the service facility. What is the average arrival rate of broken copiers to the service facility?

b. 0.2

Based on the following regression output, what proportion of the total variation in Y is explained by X?

b. 0.841282

What is the formula for P(t ≤ T) under the exponential distribution with rate μ?

b. 1 − e−μT

Refer to Exhibit 10.1. What number of observations is classified incorrectly?

b. 3

Refer to Exhibit 10.2. What is the verbal test score value of the group centroid for group 3?

b. 605.17

Refer to Exhibit 11.2. What would be the forecasted value for time period 13?

b. 83.024.

Refer to Exhibit 11.9. What formula should be entered in cell E3 to compute the linear trend for year 1 Quarter 1?

b. = 114.1364 + 69.7902 * 1

Refer to Exhibit 11.10. What formula should be entered in cell F3 to compute the quadratic trend for year 1 Quarter 1?

b. = 263.4545 + 5.985514 * C3 + 4.922577 * D3

A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. Years to InvestmentReturnMaturityRatingA6.45%91-ExcellentB7.10%82-Very GoodC8.20%54-FairD9.00%83-Good LetX1 = Dollars invested in A X2 = Dollars invested in B X3 = Dollars invested in C X4 = Dollars invested in D MAX:.0645 X1 + .071 X2 + .082 X3 + .09 X4Subject to:X1 + X2 + X3 + X4 ≤ 300000 X1 ≤ 75000 X2 ≤ 75000 X3 ≤ 75000 X4 ≤ 75000 X1 + X2 + X4 ≥ 100000 X3 + X4 ≤ 75000 X1, X2, X3, X4 ≥ 0 ABCD>1 AmountMaximum >2BondInvested25.00%Return>3A$0$75,0006.45%>4B$0$75,0007.10%>5C$0$75,0008.20%>6D$0$75,0009.00%>7 Total Invested:$0Total:$0>8 Total Available:$300,000 > < EFGH<1Years to7+ years? Good or worse?<2Maturity(1-yes, 0-no)Rating(1-yes, 0-no)<3911-Excellent0<4812-Very Good0<5504-Fair1<6813-Good1<7 Total:$0 Total:$0<8 Required:$100,000 Allowed:$75,000 Refer to Exhibit 3.4. What formula should be entered in cell D7 in the accompanying Excel spreadsheet to compute the total return?

b. =SUMPRODUCT(B3:B6,D3:D6)

Which of the following is false regarding a goal constraint?

b. A goal constraint will always contain two deviational variables.

Decision-making problems which can be stated as a collection of desired objectives are known as what type of problem?

b. A goal programming problem.

The goal of discriminant analysis is

b. to develop a rule for predicting to what group a new observation is most likely to belong.

A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. Which cell(s) in the spreadsheet represent the decision variables in the problem? A B C D 1 2 X-Coordinate Y-Coordinate 3 Warehouse 163.800 101.000 Distance: 4 Store 1 100 130 70.082 5 Store 2 90 60 84.424 6 Store 3 210 80 50.749 7 Store 4 180 110 18.532 8 9 Total Distance: 223.787

b. B3:C3

How are binary variables specified in the Analytic Solver Platform (ASP)?

b. By specifying changing cells as BINARY in the Variable Type/Bound area of ASP.

Which point or points are global optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

b. D

The following questions are based on the problem below.A company wants to advertise on TV and radio. The company wants to produce about 6 TV ads and 12 radio ads. Each TV ad costs $20,000 and is viewed by 10 million people. Radio ads cost $10,000 and are heard by 7 million people. The company wants to reach about 140 million people, and spend about $200,000 for all the ads. The problem has been set up in the following Excel spreadsheet. A B C D E 1 Problem Data TV Radio 2 Cost 20 10 3 Coverage 10 7 4 5 Goal Constraints TV Radio Cost Coverage 6 Actual Amount 0 0 7 +Under 0 0 0 0 8 − Over 0 0 0 0 9 = Goal 0 0 0 0 10 Target Value 6 12 200 140 11 12 Percentage Deviation: 13 Under 1 1 1 1 14 Over 0 0 0 0 15 16 Weights 17 Under 18 Over 19 20 Objective 0 Refer to Exhibit 7.1. If the company is very concerned about going over the $200,000 budget, which cell value should change and how should it change?

b. D14, increase

A sub-problem in a B & B is solved and found infeasible. Should the B & B algorithm continue further analysis on this candidate problem?

b. No, adding more constraints will not restore problem feasibility.

Which type of spreadsheet cell represents the objective function in an LP model?

b. Objective cell

What does the Analytic Solver Platform integer tolerance factor of 0 accomplish?

b. Stops B & B when the true optimal integer solution has been found.

What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?

b. The model solution is not guaranteed to be integer.

Which of the following is a reason to employ queuing theory?

b. To reduce customer wait time in line.

Why do we create a scatter plot of the data in regression analysis?

b. To visually check for a relationship between X and Y.

The best-case analysis approach to risk analysis

c. is optimistic

A manager wants to ensure that he does not exceed his budget by more than $1000 in a goal programming problem. If the budget constraint is the third constraint in the goal programming problem which of the following formulas will best ensure that the manager's objective is met?

b. d3+ ≤ 1000

Benefits of sensitivity analysis include all the following except:

b. fosters managerial acceptance of the optimal solution.

The global optimum solution to a nonlinear programming problems (NLP), in which the objective function must be maximized, is:

b. is larger or equal to the local optimum solution

A ______________ provides a visual summary of the improvements that a data mining project provides on a binary classification problem compared to a random guess

b. lift chart

Risk needs to be analyzed using models in order to

b. make decisions better than those based on informed guesses

When a solution is degenerate the shadow prices and their ranges

b. may be interpreted in the usual way but they may not be unique.

Uncertainty

c. is the most difficult thing about decision-making

Overfitting refers to

b. placing too much emphasis on the sample-specific noise

If chance or uncertainty is present in a system then there is an element of ____ in the decision-making problem.

b. risk

In the equation Y = β 0 + β 1 X 1i + ε, β 1 is

b. the slope of the regression line

The total sum of squares (TSS) is best defined as

b. the total variation of Y around its mean.

The scores in a scoring model can be thought of as subjective assessments of

b. utility.

The "Analyze Without Solving" tool in Analytic Solver Platform is useful for

b. verifying the equations in a spreadsheet model.

Based on the following regression output, what conclusion can you reach about β 0?

b. β0 ≠ 0, with P-value = 0.016353

You want to conduct a hypothesis test for β 1. Based on the following regression output, what conclusion can you reach about β 1? Regression Statistics Multiple R 0.917214 R Square 0.841282 Adjusted R Square 0.821442 Standard Error 9.385572 Observations 10 ANOVA df SS MS F Significance F Regression 1 3735.3060 3735.30600 42.40379 0.000186 Residual 8 704.7117 88.08896 Total 9 4440.0170 Coefficients Standard Error t Stat P-value Lower 95% Intercept 31.623780 10.44297 3.028236 0.016353 7.542233 X Variable 1 1.131661 0.1737860 6.511819 0.000186 0.730910

b. β1 ≠ 0, with P-value = 0.000186

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following flowchart depicts this problem. What is the balance of flow constraint for node 7 (Diesel)?

c. .90 X37 + .95 X47 = 75

Refer to Exhibit 11.4. What formula should be entered in cell F7 to compute the seasonal factor using the additive seasonal effects model?

c. =$J$4*(D7-E7)+(1-$J$4)*F3

A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. What formula goes in cell D9 of the spreadsheet? A B C D 1 2 X-Coordinate Y-Coordinate 3 Warehouse 163.800 101.000 Distance: 4 Store 1 100 130 70.082 5 Store 2 90 60 84.424 6 Store 3 210 80 50.749 7 Store 4 180 110 18.532 8 9 Total Distance: 223.787

c. =SUM(D4:D7)

What is the search path for the following feasible solution space? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

c. A, B, C, D

If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?

c. Apply integer programming techniques.

Refer to Exhibit 14.3. What decision should be made according to the expected regret decision rule?

c. C

If no other feasible solution to a multi-objective linear programming (MOLP) problem allows an increase in any objective without decreasing at least one other objective, the solution is said to be

c. Pareto optimal.

What is the significance of an absolute cell reference in Excel?

c. The cell reference will not change if the formula containing the reference is copied to another location

Which of the following statements is false concerning either of the Allowable Increase and Allowable Decrease columns in the Sensitivity Report?

c. The values equate the decision variable profit to the cost of resources expended.

When might a network flow model for a transportation/assignment problem be preferable to a matrix form for the problem?

c. When the problem is large and not fully connected.

A wedding caterer has several wine shops from which it can order champagne. The caterer needs 100 bottles of champagne on a particular weekend for 2 weddings. The first supplier can supply either 40 bottles or 90 bottles. ​ The relevant decision variable is defined as ​ X1 = the number of bottles supplied by supplier 1 ​ Which set of constraints reflects the fact that supplier 1 can supply only 40 or 90 bottles?

c. X1 = 40Y11 + 90Y12, Y11 + Y12 ≤ 1

An analyst has identified 3 independent variables (X 1, X 2, X 3) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R 2 value for the X 3 model the same as the R 2 value for the X 1 and X 3 model, but the Adjusted R 2 values differ? IndependentVariable in theModel R2 Adjusted R2 Se Parameter EstimatesX1 0.00089 −0.1240 23.5480 b0 = 93.7174, b1 = 0.922X2 0.38700 0.3104 18.4480 b0 = 57.0803, b2 = 1.545X1 and X2 0.39100 0.2170 19.6540 b0 = 50.2927, b1 = 1.952, b2 = 1.554X3 0.84130 0.8214 9.3858 b0 = 31.6238, b3 = 1.132X1 and X3 0.84130 0.7960 10.0330 b0 = 31.133, b1 = 0.148, b3 = 1.132X2 and X3 0.98630 0.9824 2.9480 b0 = 14.169, b2 = 0.985, b3 = 0.995All three 0.98710 0.9807 3.0850 b0 = 11.113, b1 = 0.899, b2 = 0.990, b3 = 0.993

c. X1 does not reduce ESS enough to compensate for its addition to the model.

What is the constraint for node 2 in the following maximal flow problem?

c. X12 − X23 − X24 = 0

In solving the NLP problem, Solver produced a message "Solver found a solution. All constraints and optimality conditions are satisfied." This means that Solver found:

c. a local optimal solution

In NLP a local optimum is best described as

c. a point yielding no improving direction.

What needs to be done to the two constraints in order to convert the problem to a standard form? MAX:8 X1 + 4 X2 Subject to: 5 X1 + 5 X2 ≤ 20 6 X1 + 2 X2 ≤ 18 X1, X2 ≥ 0

c. a slack variable needs to be added to each constraint to convert them to equalities.

NLP problems which have slack in all the constraints

c. are at an interior point of the feasible region.

Meaningful Analytic Solver Platform (ASP) sensitivity report headings can be defined

c. by carefully labeling rows and columns in the spreadsheet model.

The d i +, d i − variables are referred to as

c. deviational variables.

Which decision rule pessimistically assumes that nature will always be "against us" regardless of what decision we make?

c. maximin decision rule.

A correlation coefficient

c. measures the strength of a linear association between two variables

The MINIMAX objective

c. minimizes the maximum deviation from any goal.

The street intersections in a city road network represent

c. nodes.

A time series which has a significant upward or downward trend is referred to as

c. non-stationary.

A nonzero reduced gradient value indicates the approximate impact

c. on the objective function of very small changes in the value of a given variable

The first step in creating a classification tree involves

c. recursively partitioning the independent variables using the outcome of previous partitions

The amount of opportunity lost in making a decision is called

c. regret.

Seasonality is defined as

c. regular variation above and below the trend line with a cycle completing itself within a year

Seasonality in a time series is indicated by

c. regular, repeating patterns in the data around a trend line.

A Poisson distribution shape can be described as

c. skewed to the right.

In the GRG algorithm the initial solution is called the

c. starting point.

The allowable increase for a constraint is

c. the amount by which the resource can increase given shadow price.

In regression analysis, the total variation is:

c. the sum of the explained variation and unexplained variation

An arrival process is memoryless if

c. the time until the next arrival does not depend on the time elapsed since the last arrival.

The M/M/s model with finite capacity queue can be used to model

c. traffic in a dentist's office

To find steady-state values for the M/M/S queuing system, which of the following statements must be true about the arrival rate?

c. λ < s μ

A purely rational decision maker should

consistently select the same alternative, regardless of how the problem is framed.

Exhibit 7.2The following questions are based on the problem below.An investor has $150,000 to invest in investments A and B. Investment A requires a $10,000 minimum investment, pays a return of 12% and has a risk factor of .50. Investment B requires a $15,000 minimum investment, pays a return of 10% and has a risk factor of .20. The investor wants to maximize the return while minimizing the risk of the portfolio. The following multi-objective linear programming (MOLP) has been solved in Excel. A B C D 1 Problem data A B 2 Expected return 12% 10% 3 Risk rating 0.50 0.20 4 5 Variables A B Total 6 Amount invested 0 0 0 7 Minimum required $10,000 $15,000 $150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 Refer to Exhibit 7.2. Which cell(s) is(are) the target cells in this model?

d. $B$10:$B$11

The following questions are based on the problem below.A company wants to advertise on TV and radio. The company wants to produce about 6 TV ads and 12 radio ads. Each TV ad costs $20,000 and is viewed by 10 million people. Radio ads cost $10,000 and are heard by 7 million people. The company wants to reach about 140 million people, and spend about $200,000 for all the ads. The problem has been set up in the following Excel spreadsheet. A B C D E 1 Problem Data TV Radio 2 Cost 20 10 3 Coverage 10 7 4 5 Goal Constraints TV Radio Cost Coverage 6 Actual Amount 0 0 7 +Under 0 0 0 0 8 − Over 0 0 0 0 9 = Goal 0 0 0 0 10 Target Value 6 12 200 140 11 12 Percentage Deviation: 13 Under 1 1 1 1 14 Over 0 0 0 0 15 16 Weights 17 Under 18 Over 19 20 Objective 0 Refer to Exhibit 7.1. Which cells are the variable cells in this model?

d. $B$6:$C$6, $B$7:$E$8

An investor has $150,000 to invest in investments A and B. Investment A requires a $10,000 minimum investment, pays a return of 12% and has a risk factor of .50. Investment B requires a $15,000 minimum investment, pays a return of 10% and has a risk factor of .20. The investor wants to maximize the return while minimizing the risk of the portfolio. The following multi-objective linear programming (MOLP) has been solved in Excel. A B C D 1 Problem data A B 2 Expected return 12% 10% 3 Risk rating 0.50 0.20 4 5 Variables A B Total 6 Amount invested 0 0 0 7 Minimum required $10,000 $15,000 $150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 Refer to Exhibit 7.2. What Analytic Solver Platform constraint involves cells $B$6:$C$6?

d. $B$6:$C$6≥$B$7:$C$7

Refer to Exhibit 11.9. What are predicted sales for the fourth quarter of year 4?

d. 1230 ≤ predicted sales < 1235

Suppose that the regrets for an alternative with three states of nature are: 20, 10, and 0. The probabilities of these states of nature are 0.2, 0.3, and 0.5, respectively. The expected regret for the alternative is equal to

d. 7

Refer to Exhibit 11.4. What formula should be entered in cell E7 to compute the remaining expected levels?

d. =$J$3*(D7-D3) + (1-$J$3)*E6

Refer to Exhibit 11.12. What formula should be entered in cell E3 to compute the value for the indicator variable for year 1 Quarter 1?

d. =IF($B3=E$2,1,0)

A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. What formula goes in cell D4 of the spreadsheet? A B C D 1 2 X-Coordinate Y-Coordinate 3 Warehouse 163.800 101.000 Distance: 4 Store 1 100 130 70.082 5 Store 2 90 60 84.424 6 Store 3 210 80 50.749 7 Store 4 180 110 18.532 8 9 Total Distance: 223.787

d. =SQRT((B4-$B$3)^2+(C4-$C$3)^2)

Consider the equipment replacement problem presented in the chapter. Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j. How could the network model below be modified to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window? ​

d. Add a dummy node, 6, so that arc 4-6 represents just the operating costs.

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

d. An upper bound.

Refer to Exhibit 11.10. What is the Input X Range in the Regression command settings dialog box?

d. C3:D14

Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit. LetX1 = Number of liters of product A in total blend delivered X2 = Number of liters of product B in total blend delivered MIN:7 X1 + 3 X2Subject to:X1 + X2 = 1.5 * 50 (Total liters of mix) X1 ≥ 0.48 * 1.5 * 50 (X1 minimum) X2 ≥ 0.5 * 50 (X2 minimum) .0.95 X1 + 0.78 X2 ≥ 0.85 * 1.5 * 50 (85% alcohol minimum) X1, X2 ≥ 0 ABCDE1 Jacks' Distillery 2 3 AB 4Liters to use Total Cost:5Unit cost:10.54.5 6 7Constraints: SuppliedRequirement8Total Liters11 759A required1 3610B required 1 251185% alcohol0.950.78 63.752 3 AB 4Liters to use Total Cost:5Unit cost:10.54.5 6 7Constraints: SuppliedRequirement8Total Liters11 759A required1 3610B required 1 251185% alcohol0.950.78 63.75

d. D8 = E8

Useful data mining techniques can be found in Excel under ___________ drop menu

d. Data/(Data Analysis)

Decision analysis supports all but one of the following goals. Which goal is not supported?

d. Ensure selection of good outcomes.

What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

d. Indicates unmet demand at demand nodes

In a transshipment problem, which of the following statements is a correct representation of the balance-of-flow rule if Total Supply < Total Demand?

d. Inflow − Outflow ≤ Supply or Demand

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

d. LP relaxation.

The M in M/G/1 stands for

d. Markovian inter-arrival times.

Refer to Exhibit 10.1. Suppose that for a given observation, the difference between Mahalanobis distances between group 1 and 2 (G1-G2) is small. This means that

d. The observation is likely to be classified incorrectly

In general there are two primary issues involved in risk. What are these two issues?

d. Uncertainty of the outcome and magnitude of the potential loss.

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. Hours required by Operation A B Hours Cutting 3 4 48 Welding 2 1 36 The decision variables are defined asXi = the amount of product i producedYi = 1 if Xi > 0 and 0 if Xi = 0Which of the following constraints creates the link between setting up to produce A's and making some A's for this problem?

d. X1 ≤ 16Y1

Binary variables are:

d. a subset of integer variables

The adjusted R 2 statistic

d. adjusts R2 for the degrees of freedom in the multiple regression model

A solution to the system of equations using a set of basic variables is called

d. basic feasible solution.

The optimal trade-off between risk and return for a given portfolio problem can be summarized by the

d. efficient frontier.

The "Objective Value of" option in the Analytic Solver Platform task pane may be used to

d. find a solution for a specific objective function value.

A network flow problem that allows gains or losses along the arcs is called a

d. generalized network flow model.

The primary benefit of a MINIMAX objective function is

d. it yields a larger variety of solutions than generally available using an LP method.

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the optimal solution?

d. no change

The constraints X 1 ≥ 0 and X 2 ≥ 0 are referred to as

d. nonnegativity conditions.

The reduced cost for a changing cell (decision variable) is

d. the per unit profits minus the per unit costs for that variable.

R 2 measures

d. the percentage of variability in the dependent variable, Y, explained by the model

The main difference between shadow prices and Lagrange multipliers is

d. the range of RHS values over which the Lagrange multipliers or the shadow prices remain valid

The actual value of a dependent variable will generally differ from the regression equation estimate due to

d. unaccounted for random variation.

A good way to fit the distribution to historical patterns when historical data is available is to

d. use the Fit icon in the Tools group of the Analytic Solver Platform

The "Analyze Without Solving" tool in Analytic Solver Platform is useful for

d. verifying the equations in a spreadsheet model.

The shadow price of a nonbinding constraint is

d. zero

The number of units to ship from Chicago to Memphis is an example of a(n)

decision

A production optimization problem has 4 decision variables and a requirement that at least b 1 units of material 1 are consumed. Which of the following constraints reflects this fact?

f(X1, X2, X3, X4) ≥ b1

Chapter One discussed all of the following except:

how to implement a problem formulation as a spreadsheet model.

Business analytics focuses on

identifying and leveraging business opportunities.

In a spreadsheet, input cells correspond conceptually to

independent variables.

A factor that plays a role in determining whether a good or bad outcome occurs is called

luck

Retail companies try to find

the least costly method of transferring goods from warehouses to stores.