Question 1

An uncertain future event affecting the consequence associated with a decision is known as a

Accepted Answer

A) chance event. 
B) decision alternative. 
C) decision node. 
D) payoff. 
A) chance event. 
B) decision alternative. 
C) decision node. 
D) payoff.

Question 2

A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return of investment from the mall. The profit payoff table for management (in millions of dollars) after 5 years is provided below.
​
​ $$\begin{array} { | c | c | c | c | } 
\hline && { \text { Number of Visitors } } \
\hline \text { Size of the Mall } & \text { High } & \text { Moderate } & \text { Low } \
\hline \text { Large } & 25 & 15 & - 20 \
\hline \text { Medium } & 20 & 12 & - 10 \
\hline \text { Small } & 15 & 13 & 5 \
\hline
\end{array}$$ ​
The probabilities for the state of nature are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25. 
a. A test market study of the potential response for the mall in that area is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|High) = 0.35; P(U|High) = 0.65
P(F|Moderate) = 0.45; P(U|Moderate) = 0.55
P(F|Low) = 0.20; P(U|Low) = 0.80
What is the probability that the market research report will be favorable?
b. Show the decision tree for this problem.

Accepted Answer

a. Let d₁ = Size of the shopping mall i

Question 3

The following payoff table shows the profit for a decision problem with three states of nature and three decision alternatives: $$\begin{array} { | l | c | c | c | } 
\hline \text { Decision } &  { \text { State of Nature } } \
\hline  \text { Alternative } & \boldsymbol { s 1 } & \boldsymbol { s 2 } & \boldsymbol { s 3 } \
\hline \boldsymbol { A 1 } & 7 & 3 & 4 \
\hline \boldsymbol { d } & 2 & 4 & 5 \
\hline \boldsymbol { d } & 8 & 2 & 3 \
\hline
\end{array}$$ 
a. Suppose P(s1) = 0.1, P(S2) = 0.3, and P(S3) = 0.6. What is the best decision using the expected value approach?
b. Suppose that the probability of sate of nature, s1, s2, and s3 changes to 0.4, 0.2, and 0.4, respectively. What is the best decision using the expected value approach in this case?

Accepted Answer

a. EV(d₁) = 0.1(7) + 0.3(3) + 0.6(4) =

Question 4

_____________ are possible outcomes for chance events that affect the consequences associated with a decision alternative.

Accepted Answer

A) Payoffs 
B) Forecasts 
C) Decision trees 
D) States of nature 
A) Payoffs 
B) Forecasts 
C) Decision trees 
D) States of nature

Question 5

For a maximization problem, the conservative approach often is referred to as the __________ approach.

Accepted Answer

A) maximin 
B) maximax 
C) minimax 
D) minimin 
A) maximin 
B) maximax 
C) minimax 
D) minimin

Question 6

For a minimization problem, the conservative approach often is referred to as the __________ approach.

Accepted Answer

A) maximin 
B) minimax 
C) minimin 
D) maximax 
A) maximin 
B) minimax 
C) minimin 
D) maximax

Question 7

The states of nature are defined so that they are ___________. This means that at least one state of nature must occur at a given time for a chance event.

Accepted Answer

A) collectively exhaustive 
B) mutually exclusive 
C) certain events 
D) optimistic outcomes 
A) collectively exhaustive 
B) mutually exclusive 
C) certain events 
D) optimistic outcomes

Question 8

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as

Accepted Answer

A) joint probability. 
B) sample information. 
C) conditional probability. 
D) expected utility. 
A) joint probability. 
B) sample information. 
C) conditional probability. 
D) expected utility.

Question 9

The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River Basin. The mining company is considering two payment-plan options to buy the mines:
I. 100% Payment
II. Installment-Payment
The payoff received will be based on the quality of coal obtained from the mines which has been categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in million dollars resulting from the various combinations of options and quality are provided below: $$\begin{array} { | l | c | c | c | } 
\hline  { \text { Payment-Plan Options } } & & { \text { Quality } } & \
\hline  & \text { High } & \text { Normal } & \text { Poor } \
\hline \mathbf { 1 0 0 \% } \text { Payment } & 450 & 320 & - 250 \
\hline \text { Installment-Payment } & 350 & 300 & - 110 \
\hline
\end{array}$$ 
a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event?
b. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Accepted Answer

​
a. The decision to be made is to choos

Question 10

___________ refer to graphical representations of the decision problems that show the sequential nature of the decision-making process.

Accepted Answer

A) Influence diagrams 
B) Utility functions 
C) Decision trees 
D) Payoff tables 
A) Influence diagrams 
B) Utility functions 
C) Decision trees 
D) Payoff tables

Question 11

A(n) _________ refers to the result obtained when a decision alternative is chosen and a chance event occurs.

Accepted Answer

A) payoff table 
B) outcome 
C) state of nature 
D) node 
A) payoff table 
B) outcome 
C) state of nature 
D) node

Question 12

Bayes' theorem

Accepted Answer

A) can be used only for cases where conditional probabilities are unknown. 
B) cannot be used to calculate posterior probabilities. 
C) enables the use of sample information to revise prior probabilities. 
D) is useful for determining optimal decisions without requiring knowledge of probabilities of the states of nature. 
A) can be used only for cases where conditional probabilities are unknown. 
B) cannot be used to calculate posterior probabilities. 
C) enables the use of sample information to revise prior probabilities. 
D) is useful for determining optimal decisions without requiring knowledge of probabilities of the states of nature.

Question 13

Meega airlines decided to offer direct service from Akron to Clearwater Beach, Florida. Management must decide between full-price service using a company's new fleet of jet aircraft and a discount-service using smaller capacity commuter planes. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service on Clearwater Beach: high, moderate, and low. The following table shows the estimated quarterly profits (in thousands of dollars).
​
​ $$\begin{array} { | l | c | c | c | } 
\hline  { \text { Service } } & & { \text { Demand for service } } \
\hline  & \text { High } & \text { Medium } & \text { Low } \
\hline \text { Full price } & 900 & 760 & - 430 \
\hline \text { Discount } & 710 & 650 & 350 \
\hline
\end{array}$$ ​
The probabilities for the demand is P(High) = 0.3, P(Medium) = 0.5, and P(Low) = 0.2, respectively. 
a. What is the optimal decision strategy if perfect information were available?
b. What is the expected value for the decision strategy developed in part a?
c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?
d. What is the expected value of perfect information?

Accepted Answer

a. If demand is High or Medium, select t

Question 14

Using the Table below, which is the recommended decision alternative using the conservative approach? $$\begin{array}{l}
\text { Payo ff Table }\
\begin{array} { | c | c | c | } 
\hline \text { Decision Alternative } & \text { State of Nature 1 } & \text { State of Nature 2 } \
\hline \text { D1 } & 5 & 7 \
\hline \text { D2 } & - 4 & 1 \
\hline \text { D3 } & 1 & - 3 \
\hline \text { D4 } & 10 & 2 \
\hline \text { D5 } & 6 & 4 \
\hline
\end{array}
\end{array}$$

Accepted Answer

A) D1 
B) D5 
C) D2 
D) D3 
A) D1 
B) D5 
C) D2 
D) D3

Question 15

Consider a decision situation with four possible states of nature: s1, s2, s3, and s4. The prior probabilities are P(s1) = 0.35, P(s2) = 0.15, P(s3) = 0.20, P(s4) = 0.30. The conditional probabilities are P(C|s1) = 0.2, P(C|s2) = 0.09, P(C|s3) = 0.15, and P(C|s4) = 0.20. Find the revised (posterior) probabilities P(s1|C), P(s2|C), P(s3|C), and P(s4|C).

Accepted Answer

Question 16

The minimax regret approach is

Accepted Answer

A) purely optimistic. 
B) purely conservative. 
C) both purely optimistic and purely conservative. 
D) neither purely optimistic nor purely conservative. 
A) purely optimistic. 
B) purely conservative. 
C) both purely optimistic and purely conservative. 
D) neither purely optimistic nor purely conservative.

Question 17

Brit wants to sell throw blankets for the holiday season at a local flea market. Brit purchases the throws for $15, and sells them to his customers for $35. The rental space is fixed fee of $1500 for the season. Assume there is no leftover value for unsold units. The payoff, if he orders 200 and Demand is 150, is

Accepted Answer

A) 800. 
B) 50. 
C) 1050. 
D) 2800. 
A) 800. 
B) 50. 
C) 1050. 
D) 2800.

Question 18

Using the data below, which of the following would be the posterior probabilities, P(Sj|U)? ?
? $$\begin{array} { c c c } 
& \begin{array} { c } 
\text { Prior } \
\text { Probabilities }
\end{array} & \begin{array} { c } 
\text { Conditional } \
\text { Probabilities }
\end{array} \
\text { States of Nature } ( S j ) & P ( S j ) & P ( U \mid S j ) \
\hline S 1 & 0.65 & 0.75 \
S 2 & 0.20 & 0.35 \
S 3 & 0.15 & 0.20 \
\hline \text { Total } & 1.00 & \
\hline
\end{array}$$ ?

Accepted Answer

A) 0.83, 0.12, and 0.05 
B) 0.49, 0.07, and 0.03 
C) 0.47, 0.49, and 0.04 
D) 1.00, 0.59, and 1.00 
A) 0.83, 0.12, and 0.05 
B) 0.49, 0.07, and 0.03 
C) 0.47, 0.49, and 0.04 
D) 1.00, 0.59, and 1.00

Question 19

Jasen Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Jasen a 24-month lease with no down payment due at the time of signing. Each lease includes a monthly cost, mileage allowances, and the cost for additional miles and the details are given in the below table. $$\begin{array} { | l | c | c | c | } 
\hline \text { Dealer } & \begin{array} { c } 
\text { Mon thly Cost } \
\text { (\$) }
\end{array} & \text { Mileage Allowances } & \begin{array} { c } 
\text { Cost p er } \
\text { Addition al Mile (\$) }
\end{array} \
\hline \text { True Vehicle } & 300 & 40,000 & 0.30 \
\hline \text { FCO } & 360 & 46,000 & 0.35 \
\hline \text { Jack's Auto } & 410 & 50,000 & 0.15 \
\hline
\end{array}$$ Jasen decided to choose the lease option that will minimize his total 24-month cost. He is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Jasen wants to evaluate options of driving 20,000 miles per year, 23,000 miles per year, and 25,000 miles per year. 
a. Construct a decision tree based on the payoff table constructed in the previous problem.
b. Recommend a decision based on the use of optimistic, conservative, and minimax regret approaches?

Accepted Answer

a. The payoff table for the cost is: @#IMG-DLM& @#IMG-DLM& b

Question 20

Which of the following is true of decision trees when used to solve a complex problem?

Accepted Answer

A) They provide a useful way to decompose the problem. 
B) They are used to compute a decision maker's risk tolerance. 
C) They can be converted into truth tables. 
D) They can be used only when the decision maker is risk neutral. 
A) They provide a useful way to decompose the problem. 
B) They are used to compute a decision maker's risk tolerance. 
C) They can be converted into truth tables. 
D) They can be used only when the decision maker is risk neutral.

An uncertain future event affecting the consequence associated with a decision is known as a

_____________ are possible outcomes for chance events that affect the consequences associated with a decision alternative.

For a maximization problem, the conservative approach often is referred to as the __________ approach.

For a minimization problem, the conservative approach often is referred to as the __________ approach.

The states of nature are defined so that they are ___________. This means that at least one state of nature must occur at a given time for a chance event.

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as

___________ refer to graphical representations of the decision problems that show the sequential nature of the decision-making process.

A(n) _________ refers to the result obtained when a decision alternative is chosen and a chance event occurs.

Bayes' theorem

Using the Table below, which is the recommended decision alternative using the conservative approach? Payo ff Table Decision Alternative State of Nature 1 State of Nature 2 D1 5 7 D2 -4 1 D3 1 -3 D4 10 2 D5 6 4

The minimax regret approach is

Using the data below, which of the following would be the posterior probabilities, P(S_j|U)? ? ? Prior Probabilities Conditional Probabilities States of Nature (Sj) P(Sj) P(U\midSj) S1 0.65 0.75 S2 0.20 0.35 S3 0.15 0.20 Total 1.00 ?

Which of the following is true of decision trees when used to solve a complex problem?

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Probability: an Introduction to Modeling Uncertainty

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Filters

Exam 15: Decision Analysis

An uncertain future event affecting the consequence associated with a decision is known as a

_____________ are possible outcomes for chance events that affect the consequences associated with a decision alternative.

For a maximization problem, the conservative approach often is referred to as the __________ approach.

For a minimization problem, the conservative approach often is referred to as the __________ approach.

The states of nature are defined so that they are ___________. This means that at least one state of nature must occur at a given time for a chance event.

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as

___________ refer to graphical representations of the decision problems that show the sequential nature of the decision-making process.

A(n) _________ refers to the result obtained when a decision alternative is chosen and a chance event occurs.

Bayes' theorem

Using the Table below, which is the recommended decision alternative using the conservative approach? Payo ff Table Decision Alternative State of Nature 1 State of Nature 2 D1 5 7 D2 -4 1 D3 1 -3 D4 10 2 D5 6 4

The minimax regret approach is

Using the data below, which of the following would be the posterior probabilities, P(Sj|U)? ? ? Prior Probabilities Conditional Probabilities States of Nature (Sj) P(Sj) P(U\midSj) S1 0.65 0.75 S2 0.20 0.35 S3 0.15 0.20 Total 1.00 ?

Which of the following is true of decision trees when used to solve a complex problem?

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Probability: an Introduction to Modeling Uncertainty

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Filters

Using the data below, which of the following would be the posterior probabilities, P(S_j|U)? ? ? Prior Probabilities Conditional Probabilities States of Nature (Sj) P(Sj) P(U\midSj) S1 0.65 0.75 S2 0.20 0.35 S3 0.15 0.20 Total 1.00 ?