Final Review Jeopardy

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Arizona State University *

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407

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Industrial Engineering

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Jan 9, 2024

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102

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ANOVA – Sampling ANOVA – Factorial Simulation Linear Optimization Integer & Non-Linear Optimization $200 $200 $200 $200 $200 $400 $400 $400 $400 $400 $600 $600 $600 $600 $600 $800 $800 $800 $800 $800 $1000 $1000 $1000 $1000 $1000
ANOVA - Sampling – $200 Answer: A researcher obtains the mortality rate and patient demographic information for the past 5 years, with the objective of examining the relationship between the mortality rate and the patient health information. Experiment or Observational Study?
Observational Study Back to the board ANOVA - Sampling – $200
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Answer: A teacher wants to study the effect of colored paper on exam scores by randomly assigning students to differently colored paper exams and recording their test times and scores. ANOVA - Sampling – $400 Experiment or Observational Study?
Experiment Back to the board ANOVA - Sampling – $400
Answer: ANOVA - Sampling – $600 450 475 500 525 550 575 600 625 650 Female Male Female Average: 550 Male Average: 590 How can we conclude that there is a difference in test scores between Females and Males?
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Look at the Sampling Variability Or Run ANOVA Back to the board ANOVA - Sampling – $600
Answer: ANOVA - Sampling – $800 df SS MS F Treatments ࠵? − 1 = 3 2794.39 ࠵?࠵?࠵? = ࠵?࠵?࠵? ࠵? − 1 ࠵?࠵?࠵? ࠵?࠵?࠵? Error ࠵? − ࠵? = 36 762.30 ࠵?࠵?࠵? = ࠵?࠵?࠵? ࠵? − ࠵? Total ࠵? − 1 = 39 3556.69 What does the F-statistic test?
Back to the board ANOVA - Sampling – $800 F-statistic determines if the means of the treatment groups are equal (H 0 ) or different (H a )
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Answer: ANOVA - Sampling – $1000 A better experimental design with better controls to help account for variability is to use matched sets. The matched sets are called ______________.
Blocks Back to the board ANOVA - Sampling – $1000
ANOVA – Factorial – $200 Answer: _________ is used to test whether the factors combine to affect the response.
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Factor Interaction Back to the board ANOVA – Factorial – $200
___________ is used to determine whether the factors affect the response separately. Answer: ANOVA - Factorial – $400
Factor Main Effect Back to the board ANOVA - Factorial – $400
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Answer: ANOVA - Factorial – $600 What is the difference between a block and a factor?
A factor is a variable of interest A block is a nuisance variable that you control for Back to the board ANOVA - Factorial – $600
Answer: ANOVA - Factorial – $800 We run our two-factor ANOVA to see if Caffeine (Some Caffeine and No Caffeine) and Time of Day (Morning, Early Afternoon, and Late Afternoon) effect Work Performance and here are the results. df SS MS F F 0.05 Caffeine 1 9631.27 9631.27 107.75 4.26 Time of Day 2 984.83 492.415 5.51 3.01 Caffeine*Time of Day 2 244.02 122.01 1.36 3.01 Error 94 8402.42 89.3874 Total 99 19262.54 How many observations were collected in the experiment?
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N=100 Back to the board ANOVA - Factorial – $800
Answer: ANOVA - Factorial – $1000 We run our two-factor ANOVA to see if Caffeine (Some Caffeine and No Caffeine) and Time of Day (Morning, Early Afternoon, and Late Afternoon) effect Work Performance and here are the results. df SS MS F F 0.05 Caffeine 1 9631.27 9631.27 107.75 4.26 Time of Day 2 984.83 492.415 5.51 3.01 Caffeine*Time of Day 2 244.02 122.01 1.36 3.01 Error 94 8402.42 89.3874 Total 99 19262.54 Calculate the Sum of Squares for Treatments, MST, and F-statistic.
Sum of Squares of Treatments = 9631.27 + 984.83 + 244.02 = 10860.12 Back to the board ANOVA - Factorial – $1000 MST = SST/(ab-1) = 10860.12/(2*3-1) = 2172.02 F = MST/MSE = 2172.02/89.3874 = 24.30
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Simulation – $200 Answer: Simulations are real-world representations. True or False
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True Back to the board Simulation – $200
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Answer: Simulation – $400 In a simulation, we replace a single variable with a ________________.
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Probability Distribution Back to the board Simulation – $400
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Answer: Simulation – $600 The process of determining that the computer procedure that performs the simulation calculations is logically correct is called ____________.
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Back to the board Simulation – $600 Verification
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Answer: Simulation – $800 The process of ensuring that the simulation model provides an accurate representation of a real system is called _______________.
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Validation Back to the board Simulation – $800
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What are some disadvantages to Simulations? Answer: Simulation – $1000
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• Time-consuming and expensive • Assumptions • Only approximations Back to the board Simulation – $1000
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Linear Optimization – $200 Answer: The term _____________ refers to the expression that defines the quantity to be maximized or minimized in a linear programming model.
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Objective Function Linear Optimization – $200 Back to the board
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Answer: Linear Optimization – $400 _____________ or modeling, is the process of translating a verbal statement of a problem into a mathematical statement.
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Problem Formulation Linear Optimization – $400 Back to the board
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Answer: Linear Optimization – $600 A controllable input for a linear programming model is known as a ____________.
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Decision Variable Linear Optimization – $600 Back to the board
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Answer: Linear Optimization – $800 What does the non-negativity constraint ensure?
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Ensures that the solution of the problem will contain only nonnegative values for the decision variables Linear Optimization – $800 Back to the board
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__________ is the situation in which no solution to the linear programming problem satisfies all the constraints. Answer: Linear Optimization – $1000
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Infeasibility Linear Optimization – $1000 Back to the board
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Integer & Non-Linear Optimization – $200 Answer: In binary integer linear program, the integer variables take only the values ____________.
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0 or 1 Back to the board Integer & Non-Linear Optimization – $200
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Answer: Integer & Non-Linear Optimization – $400 When solving a non-linear optimization problem, which Option in the Solver should you choose? Simplex LP GRG Nonlinear Evolutionary
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Back to the board Integer & Non-Linear Optimization – $400 GRG Nonlinear
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Answer: Integer & Non-Linear Optimization – $600 Is sensitivity analysis possible for integer linear programming problems?
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No, classic sensitivity analysis is not available for integer programs Integer & Non-Linear Optimization – $600 Back to the board
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Answer: Integer & Non-Linear Optimization – $800 In a non-linear optimization problem, which of the following is true? a) The objective function is a nonlinear function of the constraints b)All the constraints are nonlinear only when the objective is to maximize the function of the decision variables c) At least one term in the objective function or a constraint is nonlinear d)Both the objective function and the constraints must have all nonlinear terms
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c) At least one term in the objective function or a constraint is nonlinear Integer & Non-Linear Optimization – $800 Back to the board
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Answer: Integer & Non-Linear Optimization – $1000 A nonlinear function with at least one term raised to the power of two is known as a _______ function. a) Hyperbolic b) Quadratic c) Logarithmic d) Cubic
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Quadratic Integer & Non-Linear Optimization – $1000 Back to the board
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ANOVA - Sampling ANOVA – Factorial Simulation Linear Optimization Integer & Non-Linear Optimization $1200 $1200 $1200 $1200 $1200 $1400 $1400 $1400 $1400 $1400 $1600 $1600 $1600 $1600 $1600 $1800 $1800 $1800 $1800 $1800 $2000 $2000 $2000 $2000 $2000
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ANOVA - Sampling – $1200 Answer: Suppose I randomly selected five males and five females and looked at their exam scores. Let’s choose level of significance of α=0.05 (F 0.05 = 5.32) Our F-statistic was 3.98 What can we conclude?
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Back to the board ANOVA - Sampling – $1200 We fail to reject the null hypothesis that the means are equal.
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Answer: ANOVA - Sampling – $1400 df SS MS F Treatments ࠵? − 1 = 5 7928.89 ࠵?࠵?࠵? = ࠵?࠵?࠵? ࠵? − 1 ࠵?࠵?࠵? ࠵?࠵?࠵? Error ࠵? − ࠵? = 44 972.34 ࠵?࠵?࠵? = ࠵?࠵?࠵? ࠵? − ࠵? Total ࠵? − 1 = 49 8901.23 Based on the table, tell me something about the experiment…
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df SS MS F Treatments ࠵? − 1 = 5 ࠵?࠵?࠵? ࠵?࠵?࠵? ࠵?࠵?࠵? Error ࠵? − ࠵? = 44 972.34 ࠵?࠵?࠵? = ࠵?࠵?࠵? Total ࠵? − 1 = 49 8901.23 Back to the board ANOVA - Sampling – $1400 Based on the table, tell me something about the experiment… k=6, so we are comparing 6 different things n=50, so we have 50 observations
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Answer: ANOVA - Sampling – $1600 Researchers investigated whether rats could be trained to run a maze faster with various incentives. Rats were randomly assigned to one of five different inventive methods (plus one control) and randomly assigned to run different mazes. The rats were assigned the tasks of running a maze with a cheese treat at the end. One goal of the experiment was to identify if the incentive method made the rats run the maze faster than with no incentive. Identify the treatments and the dependent variable.
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Treatments: 6 groups Dependent Variable: Time it took for rat to run the maze Back to the board ANOVA - Sampling – $1600
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Answer: ANOVA - Sampling – $1800 Researchers investigated whether rats could be trained to run a maze faster with various incentives. Rats were randomly assigned to one of five different inventive methods (plus one control) and randomly assigned to run different mazes. The rats were assigned the tasks of running a maze with a cheese treat at the end. One goal of the experiment was to identify if the incentive method made the rats run the maze faster than with no incentive. Set up the Null and Alternative Hypotheses.
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H 0 : ࠵? ࠵? = ࠵? ࠵? = ࠵? ࠵? = ࠵? ࠵? = ࠵? ࠵? = ࠵? ࠵? H a : at least 2 ࠵?′࠵? differ Back to the board ANOVA - Sampling – $1800
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Answer: ANOVA - Sampling – $2000 Researchers investigated whether rats could be trained to run a maze faster with various incentives. Rats were randomly assigned to one of five different inventive methods (plus one control) and randomly assigned to run different mazes. The rats were assigned the tasks of running a maze with a cheese treat at the end. One goal of the experiment was to identify if the incentive method made the rats run the maze faster than with no incentive. The following results were reported: • F=78.25 • numerator df=5, denominator df=449 • F 0.05 =2.76 Interpret the results.
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Back to the board ANOVA - Sampling – $2000 Reject H 0 and conclude that the means differ for the incentive treatments
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ANOVA - Factorial – $1200 Answer: We run our two-factor ANOVA to see if Caffeine (Some Caffeine and No Caffeine) and Time of Day (Morning, Early Afternoon, and Late Afternoon) affect Work Performance and here are the results. df SS MS F F 0.05 Caffeine 1 9631.27 9631.27 107.75 4.26 Time of Day 2 984.83 492.415 5.51 3.01 Caffeine*Time of Day 2 244.02 122.01 1.36 3.01 Error 94 8402.42 89.3874 Total 99 19262.54 What can you say about interaction between Caffeine and Time of Day?
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Since F=1.36 < F 0.05 =3.01, we cannot conclude that factors Caffeine and Time of Day interact to affect Work Performance Back to the board ANOVA - Factorial – $1200
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Answer: ANOVA - Factorial – $1400 We run our two-factor ANOVA to see if Caffeine (Some Caffeine and No Caffeine) and Time of Day (Morning, Early Afternoon, and Late Afternoon) affect Work Performance and here are the results. df SS MS F F 0.05 Caffeine 1 9631.27 9631.27 107.75 4.26 Time of Day 2 984.83 492.415 5.51 3.01 Caffeine*Time of Day 2 244.02 122.01 1.36 3.01 Error 94 8402.42 89.3874 Total 99 19262.54 What can you say about Caffeine main effect?
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Back to the board ANOVA - Factorial – $1400 Since F=107.75 > F 0.05 =4.26, we can conclude that the two factors of Caffeine are associated with different Work Performance
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Answer: ANOVA - Factorial – $1600 We run our two-factor ANOVA to see if Caffeine (Some Caffeine and No Caffeine) and Time of Day (Morning, Early Afternoon, and Late Afternoon) affect Work Performance and here are the results. df SS MS F F 0.05 Caffeine 1 9631.27 9631.27 107.75 4.26 Time of Day 2 984.83 492.415 5.51 3.01 Caffeine*Time of Day 2 244.02 122.01 1.36 3.01 Error 94 8402.42 89.3874 Total 99 19262.54 What can you say about Time of Day main effect?
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Back to the board ANOVA - Factorial – $1600 Since F=5.51 > F 0.05 =3.01, we can conclude that the three factors of Time of Day are associated with different Work Performance
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Answer: ANOVA - Factorial – $1800 We want to determine the relationship between distance and brand of baseball bat. We decide to use six brands of baseball bats and three kinds of bats. What is our factorial design and how many Brand-Bat combinations are there?
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Back to the board ANOVA - Factorial – $1800 6x3 factorial design 18 different Brand- Bat combinations
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Answer: ANOVA - Factorial – $2000 ____________ SS(Total) df=n-1 ____________ SST df=ab-1 ____________ SS(A) df=a-1 ____________ SS(B) df=b-1 ____________ SS(AB) df=(a-1)(b-1) ____________ SSE df=n-ab Fill in the blanks for the A*B factor analysis.
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Back to the board ANOVA - Factorial – $2000 Total Sum of Squares SS(Total) df=n-1 Sum of Squares for Treatments SST df=ab-1 Main Effect Sum of Squares Factor A SS(A) df=a-1 Main Effect Sum of Squares Factor B SS(B) df=b-1 Interaction Sum of Squares Factors A and B SS(AB) df=(a-1)(b-1) Sum of Squares for Error SSE df=n-ab
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Simulation – $1200 Answer: What is a What-If Analysis?
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Considers alternative values for the random variables and computing the resulting value for the output Worst Case Base Case Best Case Back to the board Simulation – $1200
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Answer: The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as ______________. Simulation – $1400
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Back to the board Simulation – $1400 Risk Analysis
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Answer: Simulation – $1600 What inferences about a variable of interest can be drawn from the graph given below?
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Back to the board The variable is equally likely to take any value between 20 and 40 Simulation – $1600
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Answer: Simulation – $1800 The type of distribution shown in the graph below is a(n) __________ distribution.
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Normal Back to the board Simulation – $1800
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Answer: Simulation – $2000 The range of computer-generated random numbers is …. a) [- ∞ , ∞ ] b) (0, 1) c) [0, 1) d) (0, 1] e) [0, 1]
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Back to the board Simulation – $2000 c) [0, 1) From 0 up to but not including 1
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Linear Optimization – $1200 Answer: A(n) ___________ solution satisfies all the constraint expressions simultaneously.
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Feasible Back to the board Linear Optimization – $1200
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Answer: Linear Optimization – $1400 A ___________ refers to a constraint that can be expressed as an equality at the optimal solution.
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Back to the board Linear Optimization – $1400 Binding Constraint
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Linear Optimization – $1600 Answer: The slack value for binding constraints is ____________.
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Zero Back to the board Linear Optimization – $1600
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Answer: Linear Optimization – $1800 The change in the optimal objective function value per unit increase in the right-hand side of a constraint is given by the ____________.
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Back to the board Linear Optimization – $1800 Shadow Price
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Answer: Linear Optimization – $2000 The shadow price of nonbinding constraints will always be ________________.
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Back to the board Linear Optimization – $2000 Zero
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Integer & Non-Linear Optimization – $1200 Answer: Which of the following is a likely constraint for the production quantity x, given that the max you can produce is M scaled by a set up variable y? a) ࠵? ≥ ࠵?࠵? b) ࠵? ≤ ࠵?࠵? c) M࠵? ≤ ࠵? d) ࠵?࠵? ≥ ࠵?
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b) ࠵? ≤ ࠵?࠵? Production quantity x is less than equal to maximum value M times set up variable y Integer & Non-Linear Optimization – $1200 Back to the board
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Answer: Integer & Non-Linear Optimization – $1400 A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, which are used to make the rubber strips. Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. Processing one strip of Polyisoprene takes 3.5 hours on Machine-1 and 4 hours on Machine-2. Machine-1 is available 180 hours per month, and Machine-2 is available 200 hours per month. Formulate an all-integer mathematical model that will determine how many units of each type of rubber should be produced to maximize profits if the profit contributions of Butadiene and Polyisoprene are $20 and $26, respectively. Identify the Decision Variables and Objective Function.
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Decision Variables: B = Number of units of Butadiene produced P = Number of units of Polyisoprene produced Objective Function: Max 20B + 26P Integer & Non-Linear Optimization – $1400 Back to the board
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Answer: Integer & Non-Linear Optimization – $1600 A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, which are used to make the rubber strips. Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. Processing one strip of Polyisoprene takes 3.5 hours on Machine-1 and 4 hours on Machine-2. Machine-1 is available 180 hours per month, and Machine-2 is available 200 hours per month. Formulate an all-integer mathematical model that will determine how many units of each type of rubber should be produced to maximize profits if the profit contributions of Butadiene and Polyisoprene are $20 and $26, respectively. Identify the Constraints.
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Integer & Non-Linear Optimization – $1600 Back to the board Constraints: 75B + 3.5P ≤ 180 3B + 4P ≤ 200 B, P ≥ 0 and integer
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Answer: Integer & Non-Linear Optimization – $1800 Consider the objective function ࠵? = ࠵? ∗ ࠵? ! ∗ ࠵? " , where Y=total output A=total factor productivity L=labor input K=capital input ࠵? =capital input share of contribution for L ࠵? =capital input share of contribution for K Assume ࠵? =0.33, ࠵? =0.67, A=10, and each unit of labor costs $45, and each unit of capital costs $55. With $50,000 available in the budget, develop an optimization model to determine the number of units of capital and labor required in order to maximize output. Write out the objective function and constraints.
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Max ࠵?࠵? ∗ ࠵? ࠵?.࠵?࠵? ∗ ࠵? ࠵?.࠵?࠵? s.t. ࠵?࠵?࠵? + ࠵?࠵?࠵? ≤ ࠵?࠵?࠵?࠵?࠵? L,K ≥ 0 Integer & Non-Linear Optimization – $1800 Back to the board
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Jeff is willing to invest $5000 in buying shares and bonds of a company to gain maximum returns. From his past experience, he estimates the relationship between returns and investments made in this company to be: R = –2 S 2 – 9 B 2 – 4 SB + 20 S + 30 B . where, R = total returns in thousands of dollars S = thousands of dollars spent on Shares B = thousands of dollars spent on Bonds Jeff would like to develop a strategy that will lead to maximum return subject to the restriction provided on the amount available for investment. What is the value of return if $3,000 is invested in shares and $2,000 is invested bonds of the company? Answer: Integer & Non-Linear Optimization – $2000
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R = – 2 S 2 – 9 B 2 – 4 SB + 20 S + 30 B R = – 2(3 2 ) – 9(2 2 ) – 4(3)(2) + 20(3) + (30(2) R = 42 Return of $42,000 will be realized with this allocation of the investment. Integer & Non-Linear Optimization – $2000 Back to the board
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