Recall the decision tree.

$123$d$1$d$2$s$1$s$2$s$3$s$1$s$2$s$32701204512012095$

A decision tree begins at decision node $1$ and an upper and lower branch extend from this node to the right. The upper branch, labeled d$1,$ stops at chance node $2$ and an upper, middle and lower branch extend from this node to the right. The lower branch, labeled d$2,$ stops at chance node $3$ and an upper, middle and lower branch extend from this node to the right.

The branches extending from decision node $1$ from top to bottom are labeled d$1$ and d$2.$ The next set of branches from top to bottom are labeled s$1,$ s$2,$ s$3,$ s$1,$ s$2$ and s$3.$ The values to the right of these branches are $270,120,45,120,120,$ and $95$ respectively.

Using the optimistic approach, the largest maximum profit is

$270$

Correct: Your answer is correct.

by decision

d$$

Correct: Your answer is correct.

$.$

Using the conservative approach, the largest minimum profit is

$95$

Correct: Your answer is correct.

by decision

d$$

Correct: Your answer is correct.

$.$

Using the minimax regret approach, decision

d$$

Correct: Your answer is correct.

minimizes the maximum regret with a value of

$120$

Incorrect: Your answer is incorrect.

$.$