Deck 18: Decision Theory

Question 1

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

Answer 1

False

Question 2

The maximax criterion is preferred by pessimistic decision makers.

Answer 2

False

Question 3

The maximax criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum (best)possible payoff.

Answer 3

True

Question 4

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)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. The best alternative (course of action)for the EKA manufacturing company,using the maximax criterion,is alternative 1.

Question 5

When making a decision in an environment of ________________,the likelihood of each state of nature can be estimated.

A) certainty
B) uncertainty
C) risk
D) alternatives

Question 6

The expected monetary value criterion is best used when a large number of similar decisions will be made.

Question 7

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

Question 8

Maximin is a criterion used when making decisions under _____________.

A) uncertainty
B) certainty
C) risk
D) alternatives

Question 9

Maximax is a criterion used when making decisions under uncertainty.

Question 10

Maximin is a criterion used when making decisions under certainty.

Question 11

A tire manufacturer needs to choose the production level for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the level of demand (high,medium,low)is the state of nature.

Question 12

A decision maker's expected utility is based upon his/her attitude toward risk.

Question 13

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 operating in an environment of

A) certainty.
B) uncertainty.
C) risk.
D) optimism.

Question 14

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

Question 15

The ______________ is the difference between the expected payoff that would be realized if the best alternative action were selected if we knew which state of nature would occur and the expected payoff under risk.

A) maximax criterion
B) maximin criterion
C) expected utility
D) expected value of perfect information
E) expected value of sample information

Question 16

The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum of those worst possible payoffs.

Question 17

When the maximin criterion is used,the decision maker assumes that for any alternative action,the state of nature with the maximum payoff will take place.

Question 18

A set of potential future conditions that will have an effect on the results of a decision is called the states of nature.

Question 19

The maximin criterion is preferred by optimistic decision makers.

Question 20

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

A) certainty
B) uncertainty
C) risk
D) optimism

Question 21

The ____________________criterion for choosing among alternative actions assumes that the state of nature with the worst payoff will be experienced.

A) maximin
B) certainty
C) maximax
D) decision

Question 22

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)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,with probabilities of .3,.6,and .1,respectively.The payoff values are in thousands of dollars. The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.What is the maximum amount that the company would be willing to pay for perfect information?

A) $95,000
B) $112,000
C) $7,000
D) $24,000
E) $17,000

Question 23

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

A) seeking
B) averse
C) neutral
D) None of the other choices is correct.

Question 24

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

A) maximax criterion
B) maximin criterion
C) expected utility
D) expected value of perfect information
E) expected value of sample information

Question 25

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)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,with probabilities of .3,.6,and .1,respectively.The payoff values are in thousands of dollars. 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.

A) EMV₁ = $98,000,EMV₂ = $95,000,choose strategy 1
B) EMV₁ = $88,000,EMV₂ = $95,000,choose strategy 2
C) EMV₁ = $88,000,EMV₂ = $85,000,choose strategy 1
D) EMV₁ = $66,667,EMV₂ = $76,667,choose strategy 2
E) EMV₁ = $120,000,EMV₂ = $110,000,choose strategy 1

Question 26

When we assess the worth of sample information in a decision-making problem,we are performing a

A) prior analysis.
B) preposterior analysis.
C) posterior analysis.
D) payoff analysis.
E) utility analysis.

Question 27

The _____________________ criterion is attractive to those decision makers who exhibit a neutral approach toward decision choices involving risk.

A) expected utility
B) expected value
C) maximin
D) maximax
E) decision theory

Question 28

The utility curve given below represents the preferences of a _________________ decision maker.

A) risk-averse
B) risk-neutral
C) risk-seeking
D) None of the other choices is correct.

Question 29

A person's utility is determined by the preferences he/she exhibits for decision choices involving __________.

A) certainty
B) uncertainty
C) risk
D) Bayes' Theorem

Question 30

The _____________criterion finds the best-possible payoff for each alternative and then chooses the alternative that yields the maximum best-possible payoff.

A) maximin
B) certainty
C) maximax
D) decision

Question 31

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)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,with probabilities of .3,.6,and .1,respectively.The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.What is the probability that weather conditions are poor,given that the demand is high?

A) .2
B) .5
C) .8
D) .25
E) .75

Question 32

Maximax is a criterion used when making decisions under __________________.

A) certainty
B) uncertainty
C) risk
D) alternatives

Question 33

__________________ statistics is an area of statistics that uses a theorem to update prior belief about a probability or population parameter to a posterior belief.

A) Bayesian
B) Utility theory
C) Preposterior analysis
D) Risk theory

Question 34

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)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,with probabilities of .3,.6,and .1,respectively.The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.The estimated probabilities of poor weather conditions given different levels of demand are presented below. What is the probability of high demand given that the weather conditions are poor?

A) .06
B) .44
C) .1371
D) .12
E) .1818

Question 35

The expected net gain of sampling equals the expected ______________ minus the cost of sampling.

A) payoff of sampling
B) payoff of no sampling
C) value of sample information
D) value of perfect information
E) utility

Question 36

The utility curve given below represents the preferences of a _________________ decision maker.

A) risk-averse
B) risk-neutral
C) risk-seeking
D) None of the other choices is correct.

Question 37

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

A) maximin
B) certainty
C) maximax
D) decision

Question 38

The utility curve given below represents the preferences of a _________________ decision maker.

A) risk-averse
B) risk-neutral
C) risk-seeking
D) None of the other choices is correct.

Question 39

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)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. The best alternative (course of action)for the EKA manufacturing company using the maximin criterion is strategy _____ and the best possible payoff is __________.

A) 1,$50,000
B) 2,$120,000
C) 1,$100,000
D) 1,$70,000
E) 2,$80,000

Question 40

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

A) certainty
B) uncertainty
C) risk
D) alternatives

Question 41

The ____________________criterion for choosing among alternative actions assumes that the state of nature with the best payoff will be experienced.

A) maximin
B) certainty
C) maximax
D) decision

Question 42

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

A) risk
B) utility
C) certainty
D) uncertainty

Question 43

In utility theory,a(n)__________________ decision maker is an individual who will choose the decision alternative having the highest expected profit.

A) high-risk
B) low-risk
C) risk-neutral
D) posterior

Question 44

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 ____________________.

A) alternatives
B) states of nature
C) payoffs
D) perfect information

Question 45

A tire manufacturer needs to determine the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the amount of production constitutes the ___________________ actions.

A) alternative
B) utility
C) certainty
D) uncertainty

Question 46

The expected net gain of sampling equals the ____________________ minus the cost of sampling.

A) expected monetary value
B) expected value of perfect information
C) expected value of sampling information
D) expected net gain of sampling

Question 47

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)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. Determine the best alternative (course of action)for the EKA manufacturing company using the maximax criterion.

Question 48

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

A) expected monetary value
B) expected value of perfect information
C) expected value of sample information
D) expected net gain of sampling

Question 49

When applying Bayes Theorem,the sample information is combined with prior probabilities to obtain ___________________ probabilities.

A) utility
B) maximax
C) posterior
D) preposterior

Question 50

The __________________ criterion is preferred by optimistic decision makers.

A) maximax
B) maximin
C) utility theory
D) risk theory

Question 51

The expected value criterion is used for decision making under _______________.

A) risk
B) utility
C) certainty
D) uncertainty

Question 52

When we assess the worth of sample information in a decision-making problem,we are performing a(n)_____________ analysis.

A) utility
B) maximax
C) posterior
D) preposterior

Question 53

The __________________ criterion is preferred by pessimistic decision makers.

A) maximax
B) maximin
C) utility theory
D) risk theory

Question 54

The _____________________ is the difference between the expected value of sampling and the cost of sampling.

A) expected monetary value
B) expected value of perfect information
C) expected value of sample information
D) expected net gain of sampling

Question 55

The expected _____________ of a decision maker is based upon his/her attitude toward risk.

A) maximax
B) maximin
C) utility
D) risk theory

Question 56

Decision makers in business organizations make most decisions in environments that involve some degree of ___________________.

A) risk
B) utility
C) certainty
D) uncertainty

Question 57

The _______________________is the difference between the expected payoff that would have been realized had the best alternative action been selected if we knew which state of nature would occur and the expected payoff under risk.

A) expected monetary value
B) expected value of perfect information
C) expected value of sample information
D) expected net gain of sampling

Question 58

A _______________________ is a diagram that assists the decision maker in analyzing a decision problem.

A) Bayes Theorem curve
B) decision tree
C) utility curve
D) maximax table

Question 59

The _____________ criterion is best used when a large number of similar decisions will be made.

A) expected monetary value
B) expected value of perfect information
C) expected value of sample information
D) expected net gain of sampling

Question 60

The _________ curve of an individual decision maker is a plot of their utilities versus the profits.

A) utility
B) maximax
C) posterior
D) preposterior

Question 61

An automobile insurance company is in the process of reviewing its policies.The company is considering increasing the premium charged to drivers under 25.According to company records,35 percent of the insured drivers are under the age of 25.Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident.
What is the probability that an insured driver of any age will be involved in an accident?

Question 62

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Construct the revised probability table for poor weather conditions,and find the probability of high demand given that the weather conditions are poor.

Question 63

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.If the weather conditions are poor,determine which manufacturing strategy the company should implement.

Question 64

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Based on this information,the prior probabilities have been revised.If the weather conditions are favorable,P(S₁)= .4286,P(S₂)= .5357,and P(S₃)= .0357;and if the weather conditions are poor,P(S₁)= .1364,P(S₂)= .6818,and P(S₃)= .1818.It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44.Determine the expected value of sample information.What is the maximum amount that the company is willing to pay for the weather information and the additional analysis?

Question 65

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)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.Prior probabilities are .3 for s₁;.6 for s₂,and .1 for s₃. 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.

Question 66

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Based on this information,the prior probabilities have been revised.If the weather conditions are favorable,P(S₁)= .4286,P(S₂)= .5357,and P(S₃)= .0357;and if the weather conditions are poor,P(S₁)= .1364,P(S₂)= .6818,and P(S₃)= .1818.It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44.Carry out a preposterior analysis and,using the revised probabilities,determine
(1)the expected monetary value when the weather conditions are favorable and
(2)the expected monetary value when the weather conditions are poor.

Question 67

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.What is the probability that weather conditions are poor,given that the demand is high? What is the probability that weather conditions are poor,given that the demand is medium? What is the probability that weather conditions are poor,given that the demand is low?

Question 68

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Construct the revised probability table for favorable weather conditions,and find the probability of high demand given that the weather conditions are favorable.

Question 69

A pharmaceutical company manufacturing flu test kits wants to determine the probability of a teenager not having the flu when the test results indicate that they do.It is estimated that the probability of positive test for flu among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 noninfected teenagers tested as having the flu (false positive).On the other hand,1 out of 200 teenagers with the flu tested as not having the active virus (false negative).A teenager has just used the flu test kit manufactured by the company and the results showed she does not have the flu.What is the probability that she has the flu?

Question 70

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)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. Determine the best alternative (course of action)for the EKA manufacturing company using the maximin criterion.

Question 71

A pharmaceutical company manufacturing flu test kits wants to determine the probability of a teenager not having the flu when the test results indicate that they do.It is estimated that the probability of positive test for flu among potential users of the kit is 10 percent.According to the company laboratory test results,1 out of 100 noninfected teenagers tested as having the flu (false positive).On the other hand,1 out of 200 teenagers with the flu tested as not having the active virus (false negative).A teenager has just used the flu test kit manufactured by the company and the results showed she has the flu.What is the probability that she does not have the flu?

Question 72

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. What alternative action should be selected according to the maximin criterion?

Question 73

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)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. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 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 favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.If the weather conditions are favorable,determine which manufacturing strategy the company should implement.

Question 74

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. Based on historical data,if the lot is poor quality,40 percent of the items are defective.If the lot is fair quality,22 percent of the items are defective.If the lot is good quality,10 percent of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting it,he determines that the unit is not defective.Based on this additional information,determine the revised (posterior)probabilities for each of the three states of nature.

Question 75

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. What is the maximum amount that the quality control manager would be willing to pay for perfect information?

Question 76

An automobile insurance company is in the process of reviewing its policies.The company is considering increasing the premium charged to drivers under 25.According to company records,35 percent of the insured drivers are under the age of 25.Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident.An accident has just been reported.What is the probability that the insured driver is under the age of 25?

Question 77

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. What alternative action should be selected according to the expected monetary value criterion?

Question 78

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. What alternative action should be selected according to the maximax criterion?

Question 79

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)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.Prior probabilities are .3 for s₁;.6 for s₂,and .1 for s₃. What is the maximum amount that the company would be willing to pay for perfect information?

Question 80

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent 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. Based on historical data,if the lot is poor quality,40 percent of the items are defective.If the lot is fair quality,22 percent of the items are defective.If the lot is good quality,10 percent of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting it,he determines that the unit is defective.Based on this additional information,determine the revised (posterior)probabilities for each of the three states of nature.