management has decided to view the possible long$-$run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars.

$\backslash$table$[[,$Long$-$Run Demand$],[$Plant Size,Low,Medium,High$],[$Small$,450,500,500],[$Large$,350,500,800]]$

$($a$)$ What is the decision to be made, and what is the chance event for Southland's problem? The decision is to choose $].$ There are $$ alternatives. The chance event is Se $$ There are $$ possible outcomes.

$($b$)$ Construct a decision tree. $($Submit a file with a maximum size of $1MB.)$

$$ No fie chosen

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$($c$)$ Recommend a decision based on the use of the optimistic, conservative, and minimax regret approaches. The recommended decision using the optimistic approach is $$

$$

$.$ The recommended decision using the conservative approach is $$

$$ The recommended decision using the minimax regret approach is $$