TriStar plans 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. TriStar estimates that the probabilities for high and low demands over the next 10 years are .75 and .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 TriStar over the next 10 years. (For simplicity, ignore the time value of money.)

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Alternative Full-size plant now Small-size plant now Expanded plant in 2 years Annual income estimates (in $1000) High demand Low demand 1000 250 900 300 200 200