Belinda Tire and Rubber, Inc. is considering expanding production to meet

potential increases in the demand for one of its tire products. Belinda$$s

alternatives are to construct a new plant, expand the existing plant, or do nothing

in the short run. The market for this particular tire product may expand, remain

stable, or contract. Belinda$$s marketing department estimates the probabilities of

these market outcomes as $0\mathrm{.}25,0\mathrm{.}35,$ and $0\mathrm{.}4,$ respectively. Table I contains

Belinda$$s estimated payoff.

a$.$ Construct a decision tree for this problem.

b$.$ Identify the strategy that maximizes Belinda$$s expected profit.

Market Outcome $($dollars$)$

Decision Market expands Market stable Market contracts

Construct a new plant $400,000-100,000-200,000$

Expand existing plant $250,000-50,000-75,000$

Do nothing $50,0000-30,000$

Table I