$1.$ Decision Tree Analysis: Capacity Planning

A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners. The alternatives are to build a new plant, expand the old plant, or do nothing. The marketing department estimates a $\backslash (35\backslash \%\backslash )$ probability of a market upturn, a $\backslash (40\backslash \%\backslash )$ probability of a stable market, and a $\backslash (25\backslash \%\backslash )$ probability of a market downturn.

Georgia Swain, the firm's capital appropriations analyst, estimates the following annual returns for these alternatives:

$2.$ Use a decision tree analysis to analyze the decision alternatives.

$3.$ What should the company do$?$ Why?

$4.$ What returns will accrue to the company if your recommendation is followed?

$5.$ Decision Tree Analysis: Capacity Planning

a$.$ Use a decision tree analysis and recommend a course of action for this new$-$product idea.