• Max Burg is considering setting up a restaurant. If he opens it in Castle Street, he believes there is an equal chance of making a profit of £150,000 or £100,000 in the first year, depending on whether the trade is high or low. If, however, he opens a site on the High Street, then he believes he has a 70% chance of making a profit of £150,000 and a 30% chance of making a profit of £100,000 in the first year. Where should he open the restaurant if he wishes to maximize his expected profit over the first year, and what is the expected profit from his chosen course of action?
• Max is concerned about the possibility of the UK being in recession by the time the restaurant would be opened. He thinks there is a 40% chance of recession. If there is no recession, then the situation is as described in part. However, if there is a recession, then he estimates that the Castle Street restaurant would result in £20,000 profit or £30,000 loss over the first year with equal probabilities. At the High Street site, if there is a recession, he estimates he would have a 40% chance of making a profit of £100,000 and a 60% chance of losing £50,000 in the first year. Draw a decision tree for this problem. Using your decision tree determine if Max should open a restaurant if he wants to maximize his expected profit over the first year, and if so, where and what is the expected profit from this chosen course of action?
• Discuss the limitations of the decision analysis performed and whether the maximization of expected profits is a sensible criterion for Max to use when making his decision.