Refer to Chapter $13,$ page $656$ in your text. Answer problem #$3,$ questions A through D$,$ which are displayed below. It is permissible for you to download TreePlan and follow the example in Appendix $13\mathrm{.}2$ on page $683$ to answer these questions. You may also use Word, PowerPoint, or Excel to answer these questions.

Southland Corporation's decided to produce a new line of recreational products. As a result, Southland needed to build a new plant to manufacture these products. The question was how large a plant does Southland need to build? Plant size depends on how the marketplace reacts to the new product line. To conduct such an analysis, the marketing managers decided to examine the possible long$-$run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:

Payoff Table

$\backslash$table$[[$Plant Size,Long$-$Run Demand,Long$-$Run Demand,Long$-$Run Demand$],[,$Low,Medium,Large$],[$Small$,150,200,200],[$Large$,50,200,500]]$

What is the decision to be made, and what is the chance event for Southland's problem?

Construct an influence diagram.

Construct a decision tree.

Recommend a decision based on the use of an optimistic, conservative, and minimax regret approach.

In a brief narrative, explain the importance of using a decision tree to make sound decisions in business.

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