Question

1. the following is a payoff table giving profits for various situations. states of nature ... Question: 1. The following is a payoff table giving profits for various situations. &nb... 1. The following is a payoff table giving profits for various situations. States of Nature Alternatives A B C Alt-ve 1 100 120 180 Alt-ve 2 120 140 120 Alt-ve 3 200 100 50 Do Nothing 0 0 0 1. If a person were to use the expected monetary value criterion (EMV), what decision would be made? A) Alternative 1 B) Alternative 2 C) Alternative 3 D) Do Nothing 2. If a person selected Alternative 3, what would the expected profit be? A) 130 B) 120 C) 126 D) 0 3. What is the expected value of perfect information? A) 166 B) 36 C) 130 D) 120 4. What is the minimum expected opportunity loss (EOL)? A) 36 B) 46 C) 40 D) 166 5. A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected monetary value with no survey is $62,000. If the expected monetary value with the survey is $45,000, what is the expected value of sample information (EVSI)? A) $7,000 B) $62,000 C) -$7,000 D) $55,000 6. Draw a complete decision tree (show all the alternatives, state of nature, probabilities and pay off for each possible combination) and show the best alternative (what is your recommendation). 5 points

Answer 1

1)

We have to choose the best alternative out of three

firstly calculate the total payoff of three alternatives which is shown in below table

Alternatives	Status of nature			Total payoff
	A	B	C
Alt-ve 1	100	120	180	400
Alt-ve 2	120	140	120	380
Alt-ve 3	200	100	50	350
Do nothing	0	0	0	0

It is based on assumption that

given states of nature are equally likely

So the decision with maximum sum will be best/optimal decision

So alternative 1 with total payoff 400 will be choosen

2)

If person select alternative 3 we have to find the expected profit

for finding the expected profit if person select alternative 3

is given by below formula

Expected profit for alternative 3= states of nature*probability of states of nature

Here probability of states of nature are missing

let us take the values

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively

So substitute the values

Expected profit for alternative 3=200*0.3+100*0.5+50*0.2=60+50+10=120

So option B will be correct

3)

Now we have to find the expected value of perfect information

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively

Let us find the expected value of return for each alternative

Expected value of alternative 1=100*0.3+120*0.5+180*0.2=30+60+36=126

Expected value of alternative 2=120*0.3+140*0.5+120*0.2=36+70+24=130

Expected value of alternative 3=200*0.3+100*0.5+50*0.2=30+60+36=60+50+10=120

Let us choose the maximum value out of status of nature

Max Alt 1=200

Max Alt 2=140

Max Alt 3=180

Maximum Expected value=200*0.3+140*0.5+180*0.2=60+70+36=166

Expected value of perfect information(E.V.P.I)=166-130=36

Option B is correct

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