A retailer must decide whether to build a small or a large facility at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small facility is built and demand proves to be high, the manager may choose not to expand (payoff is $223,000) or to expand (payoff is $270,000). If a small facility is built and demand is low, there is no reason to expand, and the payoff is $200,000. If a large facility is built and demand proves to be low, the choice is to do nothing (payoff is $40,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff is estimated to be only $20,000; the payoff grows to $220,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is $800,000.

a) Draw a decision tree for this capacity expansion problem

b) Next analyze (i.e. solve) the tree to determine the expected payoff for each decision and event node. What is the optimal expansion strategy in this case and what is the expected payoff of this strategy?