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Exam 22: Decision Analysis

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Question 61

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Custom Home Designs Three different designs are being considered for new custom homes,and profits will depend on the combination of the custom home design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. $\text { Alernative (Design) }$ $\begin{array}{|c|ccc|}\hline \begin{array}{c}\text { State of Nature } \\\text { (Market condition) }\end{array} & a_{1} & a_{2} & a_{3} \\\hline s_{1} & \$ 30 & \$ 20 & \$ 10 \\s_{2} & \$ 19 & \$ 21 & \$ 15 \\s_{3} & \$ 11 & \$ 23 & \$ 45 \\\hline\end{array}$ Assume that the following probabilities are assigned to the three market conditions: P(s₁)= 0.1,P(s₂)= 0.6,and P(s₃)= 0.3. -{Custom Home Designs Narrative} What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

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Question 62

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The procedure for revising probabilities based upon additional information is referred to as:

A) utility theory.
B) Bernoulli's theorem.
C) central limit theorem.
D) Bayes Law.

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Question 63

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Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. $\begin{array} { | c | r c c | } \hline \text { States of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } \\\hline \boldsymbol { s } _ { 1 } & 12 & - 2 & \mathbf { g } \\\boldsymbol { s } _ { \mathbf { 7 } } & 4 & 10 & 5 \\\hline\end{array}$ -{Gross Profits Narrative} If the probability of s₁ is 0.2,the optimal alternative using EOL is ____________________.

Food Market The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature for a new food market: The prior probabilities of the states of nature are: P(s₁)= 0.2,P(s₂)= 0.3,and P(s₃)= 0.5. -{Food Market Narrative} Calculate the expected monetary value for each alternative with present information.What decision should be made using the EMV criterion?

Gas Company A payoff table for an electric company is shown below: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Altrnative}\\\begin{array} { | c | c c c c | } \hline \text { State of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } & \boldsymbol { a } _ { \mathbf { 4 } } \\\hline \boldsymbol { s } _ { 1 } & 7 & 0 & 4 & 6 \\\mathbf { s } _ { \mathbf { 2 } } & 2 & 4 & 3 & 5 \\\hline\end{array}\end{array}$ The following prior probabilities are assigned to the states of nature: P(s₁)= 0.3,P(s₂)= 0.7. -{Gas Company Narrative} Convert the payoff table to an opportunity loss table.

Food Market The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature for a new food market: The prior probabilities of the states of nature are: P(s₁)= 0.2,P(s₂)= 0.3,and P(s₃)= 0.5. -{Food Market Narrative} Convert the payoff table to an opportunity loss table.

The expected monetary value decision is always the same as the expected opportunity loss decision.

We compute the ____________________ by multiplying the probability of each state of nature by the largest payoff associated with that state of nature,then summing the resulting products.

____________________ probabilities are determined before any additional information is acquired.

Dishwasher Designs Three different designs are being considered for a new dishwasher,and profits will depend on the combination of the dishwasher design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Absrnative $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ (Design) $\begin{array}{c|ccc}\begin{array}{c}\text { State of Nature } \\\text { (Market condition) }\end{array} & a_{1} & a_{2} & a_{3} \\\hline s_{1} & \$ 30 & \$ 20 & \$ 10 \\s_{2} & \$ 19 & \$ 21 & \$ 15 \\s_{3} & \$ 11 & \$ 23 & \$ 45\end{array}$ Assume that the following probabilities are assigned to the three market conditions: P(s₁)= 0.1,P(s₂)= 0.6,and P(s₃)= 0.3. -{Dishwasher Designs Narrative} Convert the payoff table to an opportunity loss table.

Car Audio Store For a car audio store,a payoff table,the prior probabilities for two states of nature,and the likelihood probabilities are shown below: Payoff Table: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \text { Alternative }\\\begin{array} { | c | l l l | } \hline \text { state of Natura } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { 7 } & \boldsymbol { a } _ { \mathbf { 3 } } \\\hline \mathrm { s } _ { 1 } & 20 & 28 & 33 \\s _ { \mathrm { 2 } } & 32 & 29 & 25 \\\hline\end{array}\end{array}$ -{Car Audio Store Narrative} Calculate the expected value of sample information.

Video Business A high school student,who started doing videos as a hobby,is considering going into the videography business.The anticipated payoff table is: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Altrnative }\\\begin{array} { | c | c c | } \hline \text { State of Nature } & \begin{array} { c } \text { Start } \\\text { new business }\end{array} & \begin{array} { c } \text { Da Nat Start } \\\text { new busines5 }\end{array} \\\hline \text { Puar } & - \$ 12,000 & 0 \\\text { Fair } & \$ 10,000 & 0 \\\text { Super } & \$ 15,000 & 0 \\\hline\end{array}\end{array}$ The following prior probabilities are assigned to the states of nature: P(poor)= 0.4,P(fair)= 0.4,and P(super)= 0.2. -{Video Business Narrative} Calculate the expected opportunity loss for each act with present information.What decision should be made using the EOL criterion?

The expected value of perfect information (EVPI)is the difference between the expected payoff with perfect information (EPPI)and the expected monetary value (EMV^*).That is,EVPI = EPPI - EMV^*.

Power Company A payoff table for a power company is shown below: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Alternativa }\\\begin{array} { | c | c c c c | } \hline \text { State of Naturs } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 7 } } & \boldsymbol { a } _ { \mathbf { 3 } } & \boldsymbol { a } _ { \mathbf { 4 } } \\\hline \boldsymbol { s } _ { 1 } & 7 & 0 & 4 & 6 \\\mathbf { s } _ { \mathbf { 2 } } & 2 & 4 & 3 & 5 \\\hline\end{array}\end{array}$ The following prior probabilities are assigned to the states of nature: P(s₁)= 0.3,P(s₂)= 0.7. -{Power Company Narrative} What is the expected value of perfect information?

In general,the branches of a decision tree represent acts and states of nature.

Demolition Company The payoff table and the prior probabilities for three states of nature for a demolition company are shown below: $\begin{array}{l}\text { Alsrmativa }\\\begin{array} { | c | c c c | } \hline \text { State of Nature } & \boldsymbol { a } _ { 1 } & \boldsymbol { a } _ { \mathbf { 2 } } & \boldsymbol { a } _ { \mathbf { 3 } } \\\hline \mathbf { s } _ { 1 } & \mathbf { 8 0 } & 120 & 90 \\\mathbf { s } _ { \mathbf { 2 } } & 60 & 130 & 170 \\\mathbf { s } _ { \mathbf { 3 } } & 200 & 140 & 100 \\\hline\end{array}\end{array}$ Prior Probabilities: P(s₁)= 0.4,P(s₂)= 0.5,and P(s₃)= 0.1. -{Demolition Company Narrative} Set up the opportunity loss table.

Dishwasher Designs Three different designs are being considered for a new dishwasher,and profits will depend on the combination of the dishwasher design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Absrnative $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ (Design) $\begin{array}{c|ccc}\begin{array}{c}\text { State of Nature } \\\text { (Market condition) }\end{array} & a_{1} & a_{2} & a_{3} \\\hline s_{1} & \$ 30 & \$ 20 & \$ 10 \\s_{2} & \$ 19 & \$ 21 & \$ 15 \\s_{3} & \$ 11 & \$ 23 & \$ 45\end{array}$ Assume that the following probabilities are assigned to the three market conditions: P(s₁)= 0.1,P(s₂)= 0.6,and P(s₃)= 0.3. -{Dishwasher Designs Narrative} Calculate the expected opportunity loss for each design with present information.Which design should be selected in order to minimize the firm's expected loss?

Video Business A high school student,who started doing videos as a hobby,is considering going into the videography business.The anticipated payoff table is: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Altrnative }\\\begin{array} { | c | c c | } \hline \text { State of Nature } & \begin{array} { c } \text { Start } \\\text { new business }\end{array} & \begin{array} { c } \text { Da Nat Start } \\\text { new busines5 }\end{array} \\\hline \text { Puar } & - \$ 12,000 & 0 \\\text { Fair } & \$ 10,000 & 0 \\\text { Super } & \$ 15,000 & 0 \\\hline\end{array}\end{array}$ The following prior probabilities are assigned to the states of nature: P(poor)= 0.4,P(fair)= 0.4,and P(super)= 0.2. -{Video Business Narrative} Review the decisions made in the previous questions.Is this a coincidence? Explain.

Which of the following would not be considered a state of nature for a business firm?

Video Business A high school student,who started doing videos as a hobby,is considering going into the videography business.The anticipated payoff table is: $\begin{array}{l}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Altrnative }\\\begin{array} { | c | c c | } \hline \text { State of Nature } & \begin{array} { c } \text { Start } \\\text { new business }\end{array} & \begin{array} { c } \text { Da Nat Start } \\\text { new busines5 }\end{array} \\\hline \text { Puar } & - \$ 12,000 & 0 \\\text { Fair } & \$ 10,000 & 0 \\\text { Super } & \$ 15,000 & 0 \\\hline\end{array}\end{array}$ The following prior probabilities are assigned to the states of nature: P(poor)= 0.4,P(fair)= 0.4,and P(super)= 0.2. -{Video Business Narrative} Calculate the expected monetary value for each act with present information.What decision should be made using the EMV criterion?