You have the following payoff table for a decision analysis problem. Payoffs are in units of thousands of dollars of profit.

$\backslash$table$[[,$STATE OF NATURE$],[$ALTERNATIVES$,$s$\_(1),$s$\_(2),$s$\_(3)],[$d$\_(1),3,3,9],[$d$\_(2),4,7,6],[$d$\_(3),2,6,7]]$

a$.$ Which decision alternative would you choose using an optimistic approach?

b$.$ Which decision alternative would you choose using a conservative approach?

c$.$ Which decision alternative would you choose using the Minimax Regret approach?

For parts $d$ and $e,$ assume that $P(s_1)=0\mathrm{.}2,P(s_1)=0\mathrm{.}3,$ and $P(s_3)=0\mathrm{.}5.$

d$.$ Which decision alternative would you choose using the EV approach?

e$.$ What would be the value of perfect information?

$*$ There is a typo in the text right before part d$.$ It should say: $$For parts d and e$,$ assume that P$($s$1)=0\mathrm{.}2,$ P$($s$2)=0\mathrm{.}3,$ and P$($s$3)=0\mathrm{.}5.$