Problem:

Spectrum Hair Salon is considering expanding its business, as it is experiencing a large growth. The question is whether it should expand with a bigger facility than needed, hoping that demand will catch up, or with a small facility, knowing that it will need to reconsider expanding in three years. The management at Spectrum has estimated the following chances for demand:

•the likelihood of demand being high is 0.70;

•the likelihood of demand being low is 0.30.

Estimated profits for each alternative are as follows:

•large expansion has an estimated profitability of either $100,000 or $70,000, depending on whether demand turns out to be high or low;

•small expansion has a profitability of $50,000, assuming that demand is low;

•small expansion with an occurrence of high demand would require considering whether to expand further. If the business expands at this point, the profitability is expected to be $90,000. If it does not expand further, the profitability is expected to be $60,000.

Required:

Question 1) Draw a decision tree showing the decisions, chance events, and their probabilities, as well as the profitability of outcomes, and solve the decision tree.

Solve the given numerical problem and illustrate step by step calculation.