Question $3($inspired by H&L$,16\mathrm{.}3-2).$

Hello, Can you please do out this problem ato the final answer and explain the steps you take

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

$($a$)$ According to Bayes' decision rule, which alternative should be chosen?

$($b$)$ Find EVPI.

$($c$)$ You are given the opportunity to spend $$8,000$ to obtain more information about which state of nature is likely to occur. Given your answer to part $($b$),$ might it be worthwhile to spend this money?