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Exam 15: Decision Theory

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Question 31

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The quality control manager for the NKA Inc.must decide whether to accept (alternative 1) ,further analyze (alternative 2) ,or reject (alternative 3) the shipment (lot) of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁) ,50% chance that the lot is fair quality (S₂) ,and 20% chance that the lot is good quality (S₃) .Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$ Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting one unit,the manager determines that the unit is not defective.Based on this additional information,what is the revised (posterior) probability for the accept state?

A) 24
B) 52
C) 18
D) 39
E) 78

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Question 32

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The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (Si, i = 1, 2, 3) represent the levels of demand for the company products. S1, S2 and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. $\text { States of nature }$ $\begin{array} { | l | r | r | r | } \hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } } & \mathbf { s } _ { \mathbf { 2 } } & \mathbf { s } _ { \mathbf { 3 } } \\\hline \text { Strategy 1 } & 110 & 80 & 70 \\\hline \text { Strategy 2 } & 60 & 120 & 50 \\\hline\end{array}$ -Find the expected monetary value for each of the alternatives and determine the best alternative (course of action)for the EKA manufacturing company using the expected monetary value criterion.

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strategy 2
(EMV)₁ = (.3)(110)+ ...

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Question 33

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The _____________ criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

A decision-maker's expected utility is based upon their attitude towards risk.

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_i,i = 1,2,3) represent the levels of demand for the company products.S₁,S₂ and S₃ characterize high,medium,and low demand respectively.The payoff values are in thousands of dollars. $\begin{array} { l c c c } & { \text { States of nature } } \\& \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\\text { Alternative (strategy) 1 } & 10 & 80 & 70 \\\text { Alternative (strategy) 2 } & 60 & 120 & 50\end{array}$ The best alternative (course of action) for the EKA manufacturing company using the maximin criterion is strategy __ which assures a guaranteed minimum payoff of _____.

Maximax is a criterion used when making decisions under uncertainty.

The maximax criterion is preferred by pessimistic decision-makers.

An investor is looking at three possible investments: growth stock,blue chip stock,or municipal bonds.The investment performance will vary depending on the investment market condition of Bull (market rising) ,flat,or Bear (market falling) .The investment return for each investment for the corresponding market conditions is given below: $\begin{array} { | l | l | l | l | } \hline & \text { Bull } & \text { Flat } & \text { Bear } \\\hline \text { Growth Stock } & 20 & 1 & - 6 \\\hline \text { Blue Chip } & 9 & 8 & 0 \\\hline \text { Bonds } & 4 & 4 & 4 \\\hline\end{array}$ Which investment would the investor select if the maximin criterion is used?

In utility analysis,a utility curve that shows a rapid increase in utility for initial amounts of money followed by a gradual levelling off for larger amount of money is appropriate for a risk _____ decision maker.

A corn farmer has categorized the weather into three possible levels.The weather conditions will affect the timing of the harvest and the associated payoff.In this situation,the weather conditions are called the ____________________________.

In a decision-making situation,the maximum amount of money that should be spent to obtain perfect information is called the ______________________________.

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_i,i = 1,2,3)represent the levels of demand for the company products.S₁,S₂ and S₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. $\text { States of nature }$ $\begin{array} { | l | r | r | r | } \hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } } & \mathbf { s } _ { \mathbf { 2 } } & \mathbf { s } _ { \mathbf { 3 } } \\\hline \text { Strategy 1 } & 110 & 80 & 70 \\\hline \text { Strategy 2 } & 60 & 120 & 50 \\\hline\end{array}$ The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favourable weather conditions.14 of the 28 months with medium demand had favourable weather conditions.Only 1 of the 5 months with low demand had favourable weather conditions. -Construct the revised probability table for favourable weather conditions and find the probability of high demand given that the weather conditions are favourable.

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁),50% chance that the lot is fair quality (S₂),and 20% chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$ Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment. -A decision maker has prepared the following decision tree.There are two main decision alternatives (A and B).The probabilities for the states of nature are as follows: P(H)= .3,P(M)= .5,P(L)= .2,P(S)= .25,P(P)= .75.Calculate the highest expected profit for the decision maker and determine which of the two alternatives the individual should select.

The __________________ criterion is preferred by optimistic decision-makers.

When we use the expected monetary value criterion,the expected payoff equals the actual payoff that will be realized.

The expected monetary value criterion is used for decision-making under __________________.

The _______________________ is the difference between the expected payoff of sampling and the expected payoff based on expected monetary criterion and prior probabilities.

If the decision maker has no knowledge about the likelihood of any of the states of nature occurring,then it can be stated that the decision maker is making decisions under _____.

An investor is looking at three possible investments: growth stock,blue chip stock,or municipal bonds.The investment performance will vary depending on the investment market condition of Bull (market rising),flat,or Bear (market falling).The investment return for each investment for the corresponding market conditions is given below: $\begin{array} { | l | l | l | l | } \hline & \text { Bull } & \text { Flat } & \text { Bear } \\\hline \text { Growth Stock } & 20 & 1 & - 6 \\\hline \text { Blue Chip } & 9 & 8 & 0 \\\hline \text { Bonds } & 4 & 4 & 4 \\\hline\end{array}$ -Which investment would the investor select if the maximin criterion is used?

In a decision tree,the branches emanating from a decision point represent states of nature.