Assignment Problem: TriStar wants to open a new plant in Arkansas. The company can open a full-size plant now or a small size plant that can be expanded 2 years later if warranted by high demand. The time horizon for the decision problem is 10 years. Tri-star estimates that the probabilities for high and low demands over the next 10 years are 0.75 and 0.25, respectively. The cost of immediate construction is $5 million for a large plant and $1 million for a small plant. The expansion cost of a small plant 2 years from now is $4.2 million. The income from the operation over the next 10 years is given in the following table:
a) Develop the associated decision tree, given that after 2 years, TriStar has the option to expand or not expand the small plant.
b) Develop a construction strategy for Tri-Star over the next 10 years.