a$.$

The optimistic approach evaluates each decision in terms of the best possible payoff. When max profit is desired, the optimistic approach leads the decision maker to choose the alternative corresponding to the largest profit. For the optimistic approach, decision alternative d$1($max $14).$

The conservative approach evaluates each decision in terms of the worst possible payoff. Because the output measure is profit, the decision maker should choose the alternative that maximizes the minimum possible profit. For the conservative approach, decision alternative d$3($low $5).$

The minimax regret approach evaluates the decision to minimize the maximum state of regret that could occur over all possible states of nature, whereas the result is neither optimistic nor conservative. For the minimax regret approach, decision alternative d$3($minimax $5).$

d$1$

$14,14-14=0$

$9,10-9=1$

$10,11-10=1$

$5,13-5=8$

d$2$

$11,14-11=3$

$10,10-10=0$

$8,11-8=3$

$7,13-7=6$

d$3$

$9,14-9=5$

$10,10-10=0$

$10,11-10=1$

$11,13-11=2$

d$4$

$8,14-8=6$

$10,10-10=0$

$11,11-11=0$

$13,13-13=0$

d$1$

$0$

$1$

$1$

$8$

d$2$

$3$

$0$

$3$

$6$

d$3$

$5$

$0$

$1$

$2$

d$4$

$6$

$0$

$0$

$0$

b$.$

Because different approaches can sometimes lead to different decision recommendations, I would choose the approach that best suited the decision I was trying to make. As for the decision maker, he$/$she would have to do the same; understanding the approaches available and then selecting the approach that is most appropriate.

c$.$

For the optimistic approach, decision alternative d$1($low $5).$

For the conservative approach, decision alternative d$2$ or d$3($low $11).$

For the minimax regret approach, decision alternative d$2($minimax $3).$

d$1$

$14,14-8=6$

$9,10-9=1$

$10,10-8=2$

$5,5-5=0$

d$2$

$11,11-8=3$

$10,10-9=1$

$8,8-8=0$

$7,7-5=2$

d$3$

$9,9-8=1$

$10,10-9=1$

$10,10-8=2$

$11,11-5=6$

d$4$

$8,8-8=0$

$10,10-9=1$

$11,11-8=3$

$13,13-5=8$