A certain company decides at the present time to launch a certain product, the commercial life of which is estimated quite certainly in ten years. For the manufacture of the product in question, it is necessary to build a factory, raising the problem of its size, which will be conditioned by future demand. The company considers two alternatives at the initial moment:

A). Build a large capacity factory, with an initial cost of $3,000,000, in which case it will not be possible to reform it in the face of a sharp decrease in demand.

B). Build a small factory, with an initial cost of $1,300,000. Which is susceptible of extension to two years, (in case the demand had been high during them) with a cost of $ 2,200,000. If demand has been low in that first period, the company will continue to operate with the small plant.

The marketing research office has the complete assurance that, if in the first two years the demand is low, it will remain so for the remaining eight years, since substitute products will appear that will prevent the sale of the aforementioned product. If, on the other hand, the demand is high in the initial period, and the company does not expand the factory (if it opted at the initial time for the small factory) it is certain that competitors will be introduced, lowering the expected profitability.

There is a 70% chance that demand will be high during the first two years. If it is really high, there is an 86% chance that it will continue to be so for the next eight years, while the probability of it going down is 14%. The economic data for the different possibilities are estimated as follows:

For the large plant, and if the demand is high during the ten years, annual profits of $ 1,000,000 will be achieved; for reduced demand, the benefit will be $10,000 annually for each of the following ten years; if demand is high in the first period and then reduced, annual profits of $1,000,000 and $100,000, respectively, are estimated.

In the case of small plant, benefits of $ 450,000 per year are considered, during the first two years if the demand is high. In the event that you then go from high to low, the benefits for the next eight years would be $400,000. If, on the other hand, it remains high, these will be $300,000. In the case of having a reduced demand during the ten years, the benefits will be $ 400,000 per year.

In the case of Expanding the small factory, an income of $ 700,000 and $ 50,000 per year can be considered if the demands are respectively, high and low, and always referring to the third to tenth years.

QUESTION: It is desired to know the optimal strategy of action with the help of a decision tree, among those given below, depending on the different expected values found from the monetary values mentioned in the statement: a) Build a large factory b) Build a small factory and expand c) Build a small factory and not expand.