You are given the following payoff table $($in units of thousands of dollars$)$ for a decision

analysis problem:

$($a$)$ Which alternative should be chosen under the maximin payoff criterion $($show your work$)?$

$($b$)$ Which alternative should be chosen under the maximum likelihood criterion $($show your work$)?$

$($c$)$ Which alternative should be chosen under Bayes$$ decision rule $($show your work$)?$

$($d$)$ Using Bayes$$ decision rule, do sensitivity analysis graphically with respect to the prior

probabilities of states S$1$ and S$2($without changing the prior probability of state S$3)$ to determine

the crossover point where the decision shifts from one alternative to the other. Then use algebra

to calculate this crossover point.Alternative S$1$ S$2$ S$3$

A$1170280175$

A$2250140160$

Prior Probability $0\mathrm{.}30\mathrm{.}50\mathrm{.}2$

State of Nature