A retailer must decide whether to build a small or a large facility at a new location. Demand at the the locations can be either small or large with probabilities estimated to be 0.4 and 0.6 respectively. If the small facility is built and demand proves to be high, the manager may choose not to expand (pay off =\(\$ 223000\)) or to expand (pay off \(=\$ 270000\)), If a small facility is built and demand is low, there is no reason to expand and pay off is \(\$ 200000\). If a large facility is built and demand proves to be low, the choice is to do nothing (pay off \(=\$ 40000\)) or to stimulate the 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 \(\$ 20000\); the payoff grows to \(\$ 220000\) if the response is sizable. Finally if a large facility is built and demand turns out to be high, the payoff is \(\$ 800000\). Draw a decision tree, and then analyze it to determine the expected payoff for each decision and event node. Which alternative building a small facility or building a large facility has higher expected payoff?