Problem:
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 low is 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 profitability is to be $50,000.
Draw a decision tree showing the decisions, chance events, and their probabilities, as well as the profitability of outcomes and solve the decision tree
- EVsmall expansion = $?
- EVlarge expansion = $?
Decide what the bakery should do.