A new minor league baseball team is coming to town and the owners have decided to build a new stadium, either small or large. The success of the team with regard to ticket sales will be either high or low with probabilities of 0.7 and 0.3, respectively. If demand for tickets is high, the large stadium would provide a payoff of approximately $20 million. If ticket sales are low, the loss on the large stadium would be $5 million. If a small stadium is constructed, and ticket sales are low, the payoff is $1 million after deducting the cost of construction. If ticket sales are high, the team can choose to build an upper deck, or to maintain the existing facility. Expanding the stadium in this scenario has a payoff of $10 million, whereas maintaining the same number of seats has a payoff of only $3 million.
a) Draw a decision tree for this problem.
b) What should management do to achieve the highest expected payoff?
c) Explain the conditions under which decision trees can be useful.