Q. Have decided to build a new stadium, either small or large. Success of team with regard to ticket sales will be either high or low with probabilities of 0.75 also 0.25, respectively. If demand for tickets is high, large stadium would provide a payoff of approximately $20 million. If ticket sales are low, loss on large stadium would be $5 million. If a small stadium is constructed, also ticket sales are low, payoff is $1million after deducting cost of construction. If ticket sales are high, team can choose to build an upper deck, or to maintain existing facility. Expanding stadium in this scenario has a payoff of $10 million, whereas maintaining same number of seats has a payoff of only $3 million.
a) Draw a decision tree for this problem.
b) Illustrate what should management do to achieve highest expected payoff?
c) Explain conditions under which decision trees can be useful.