#44 Question (3): Answer the following problem: (10 marks)

The owners of a 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.

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, if does not expand further, the profitability is expected to be $30 000.

Required:

1. Draw a decision tree showing the decisions, chance events, and their probabilities, as well as the profitability of outcomes. (4 marks)
2. Compute the expected value of the small and large expansions. (6 marks)