Exam 22: Decision Analysis

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: Alternative state of Natura 20 28 33 32 29 25 -{Car Audio Store Narrative} Use the posterior probabilities for I₂ in the previous questions to recalculate the expected monetary value of each act,then determine the optimal act and the EMV^*.

The objective of a preposterior analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

The expected value of perfect information (EVPI)equals the largest expected opportunity loss (EOL^*).

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: Altrnative State of Nature Start new business Da Nat Start new busines5 Puar -\ 12,000 0 Fair \ 10,000 0 Super \ 15,000 0 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} Convert the payoff table to an opportunity loss table.

Power Company A payoff table for a power company is shown below: Alternativa State of Naturs 7 0 4 6 2 4 3 5 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 payoff with perfect information?

A payoff table lists the monetary values for each possible combination of the

Which of the following would be considered a state of nature for a business firm?

Maintenance Company For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below: Payoff Table: Alternative syate of Nature 80 120 90 60 130 170 200 140 100 Prior Probabilities: P(s₁)= 0.4,P(s₂)= 0.5,and P(s₃)= 0.1. Likelihood Probabilities: 0.5 0.3 0.2 0.2 0.6 0.2 0.1 0.2 0.7 -{Maintenance Company Narrative} Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome I₃.

A company that manufactures baseball gloves is contemplating whether to increase its advertising budget by $3 million for next year.If the expanded advertising campaign is successful,the company expects sales to increase by $4.8 million next year.If the advertising campaign fails,the company expects sales to increase by only $900,000 next year.If the advertising budget is not increased,the company expects sales to increase by $450,000.Identify the possible outcomes in this decision-making problem.

The minimum expected opportunity loss is also equal to the:

An opportunity loss is the difference between what the decision maker's profit for an act (alternative)is and what the profit could have been had the best decision been made.

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) State of Nature (Market condition) \ 30 \ 20 \ 10 \ 19 \ 21 \ 15 \ 11 \ 23 \ 45 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 monetary value for each design with present information.Which design should be selected in order to maximize the firm's expected profit?

Which of the following statements is correct?

Sporting Goods Store A payoff table for a clothing store is shown below. Altrnative state of Nature 25 -3 12 6 -13 13 The following prior probabilities are assigned to the states of nature: P(s₁)= 0.2,P(s₂)= 0.6,and P(s₃)= 0.2. -{Sporting Goods Store Narrative} Set up the opportunity loss table.

Worker safety laws would be considered a state of nature for a business firm.

The expected monetary value (EMV)of a decision alternative is the sum of the products of the payoffs and the state of nature probabilities.

Lingerie Store The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature for a new Lingerie store: $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Alternativa $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ (Decising) State of Nature \ 100 \ 80 \ 35 \ 20 \ 0 \ 70 \ 75 \ 55 \ 50 \ 15 -\ 30 \ 0 \ 35 \ 55 \ 60 The prior probabilities of the states of nature are: P(s₁)= 0.2,P(s₂)= 0.3,and P(s₃)= 0.5. -{Lingerie Store Narrative} Calculate the expected value of perfect information.

In general,the expected monetary values (EMV)represent possible payoffs.

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} If the probability of s₁ is 0.5,then the expected opportunity loss (EOL)for a₃ is ____________________.

Container Company A company must decide whether or not to change its packaging to a more environmentally safe material.The impact of the decision on profits depends on which of the following three possible scenarios develops in the future. Scenario 1: The media does not focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $35 million if they change their packaging now,but will make $75 million if they do not change their packaging now. Scenario 2: The media does focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $50 million if they change their packaging now,but will make $55 million if they do not change their packaging now. Scenario 3: The media does focus heavily on concerns about packaging and new laws requiring changes in packaging are passed.Under this scenario,the company will make $60 million if they change their packaging now,but will make only $15 million if they do not change their packaging now. The prior probabilities of the three scenarios are 0.3,0.5,and 0.2,respectively. -{Container Company Narrative} Set up the opportunity loss table.