$8.$ A decision maker is faced with three decision alternatives and four states of nature shown in the following profit pay off table in terms of Millions.

If the decision maker knows nothing about the probabilities of the four states of nature then what is the recommended decision using

a$)$ Optimistic approach $(2)$

b$)$ Pessimistic or Conservative approach $(2)$

c$)$ Minimum regret approach $(4)$

d$)$ If for S$1,$ S$2,$ S$3,$ and S$4$ probability is given as $0\mathrm{.}1,0\mathrm{.}4,0\mathrm{.}2,$ and $0\mathrm{.}3$ respectively then what would be the best expected pay off under risk? $(4)$

e$)$ What would be the expected value of perfect information $(3)$

$(2+2+4+4+3)$

Payoff table for three Decision alternatives and four states of nature

Decision Alternatives S$1$ S$2$ S$3$ S$4$

A $ $12$ $ $7$ $ $8$ $ $3$

B $ $9$ $ $8$ $ $13$ $ $5$

C $ $7$ $ $6$ S $9$ S $11$