VI$.(34$ pts in total$)$ Manager John is making decision in the following situation. The three decision alternatives are A$,$ B$,$ and C$.$ Probabilities of unfavorable, so$-$so$,$ and favorable economy are $\backslash (0\mathrm{.}2,0\mathrm{.}45\backslash ),$ and $0\mathrm{.}35$ respectively. The payoff table is as below:

Payoff table:

$(6-$a$)(6$ pts $)$ Make decision for John by using the method of Expected Payoff.

$($Show your calculations of expected payoffs in the table below.$)$

The best alternative is: $\backslash (\backslash$quad $\backslash )$ with the maximum expected payoff $\backslash (=\backslash )$

$(6-$b$)(2$ pts$)$ Suppose a decision maker selected alternative C as the decision, and the economy development has turned out to be "umfavorable". What would be the value of his regret?

Your answer: $($show your calculations."

$(6-$c$)(2$ pts$)$ Suppose that "perfect information" says that the future economy development will be $"$so$-$so$",$ then which alternative should the decision maker take? $($pick one$)$

a$.$ alternative A

b$.$ alternative $\backslash ($ B $\backslash )$

c$.$ alternative C

$(6-$d$)(6$ pts$)$ Compute the expected value of perfect information $($EVPI$)$ for this case.

Your answer: $($Show your calculations.$)$

$(6-$e$)(4$ pts$)$ Suppose John considers to consult an investment specialist, whose credentials show that the specialist has been correct in $\backslash (85\backslash \%\backslash )$ of his predictions. Up to how much would John pay to the specialist?

Your answer: $($Show your calculations. Keep $2$ digits after decimal point.$)(6-$f$)(8$ pts$)$ Develop the opportunity loss table $($regret table$)$ of the given payoff table, and calculate expected opportunity loss for each decision alternative.

$($Show results and your calculations in the table below$)$:

Opportunity loss table $($Regret table$)$:

Investment alternatives

Economy Development

Expected Opportunity Loss

un$-$favorable

so$-$so

favorable

Prob$=0\mathrm{.}2$

Prob$=0\mathrm{.}45$

Prob$=0\mathrm{.}35$

A

B

C

By using the method of Minimum regret criterion $($minimum opportunity loss criterion$),$ the best decision alternative is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$