The owners of Sweet-Tooth Bakery have determined that they need to expand their facility in order to meet their increased demand for baked goods. The decision is whether to expand now with a large facility or expand small with the possibility of having to expand again in five years.

The owners have estimated the following chances for demand:

• The likelihood of demand being high is 0.70. The likelihood of demand being lowis 0.30.

Profits for each alternative have been estimated as follows:

• Large expansion has an estimated profitability of either $80,000 or $50,000, depending on whether demand turns out to be high or low.

• Small expansion has a profitability of $40,000, assuming demand is low.

• Small expansion with an occurrence of high demand would require considering whether to expand further. If the bakery expands at this point, the profit- ability is to be $50,000.

(a) Draw a decision tree showing the decisions, chance events, and their probabilities, as well as the profitability of outcomes.

(b) Solve the decision tree and decide what the bakery should do.