The decision tree in Figure A.5 sho

The decision tree in Figure A.5 shows the event probability and the payoff for each of the seven alternative-event combinations. The first decision is whether to build a small or a large facility. Its node is shown first, to the left, because it is the decision the retailer must make now. The second decision node—whether to expand at a later date—is reached only if a small facility is built and demand turns out to be high. Finally, the third decision point—whether to advertise—is reached only if the retailer builds a large facility and demand turns out to be low.Analysis of the decision tree begins with calculation of the expected payoffs from right to left, shown on Figure A.5 beneath the appropriate event and decision nodes.1. For the event node dealing with advertising, the expected payoff is 160, or the sum of each event’s payoff weighted by its probability 30.31202 + 0.7122024.2. The expected payoff for decision node 3 is 160 because Advertise (160) is better than Do nothing (40). Prune the Do nothing alternative.3. The payoff for decision node 2 is 270 because Expand (270) is better than Do not expand (223). Prune Do not expand.4. The expected payoff for the event node dealing with demand, assuming that a small facility is built, is 242 3or 0.412002 + 0.6127024.5. The expected payoff for the event node dealing with demand, assuming that a large facility is built, is 544 3or 0.411602 + 0.6180024.6. The expected payoff for decision node 1 is 544 because the large facility’s expected payoff is largest.Prune Small facility