San Francisco State University
FINAL EXAM QUESTIONS
The sample problems below are organized by topic. Where possible, answers are given. Disclaimers:
• These questions are questions that have appeared on previous years’ (final) examinations. They are for practice only. There is no guarantee that the questions on your finals will be the same, or that different professors will give the same types of questions. • Not all 412/786 sections cover the same material. The questions may contain material that is unfamiliar to you, or not contain material you covered. If you have concerns about the topics for your final, talk to your professor.
• Short answer and multiple choice questions are not included in this handout. • Some questions may have been slightly modified to make them more general.
1. Sheree is deciding on how to invest her $1000 tax refund. She reads that Merck is partnering with a small biotech firm to produce a cancer drug which may or may not receive FDA approval in the next six months. If the FDA approves it, the biotech firm’s stock will double in value, but if it rejects it, the firm goes bankrupt and its stock becomes worthless. Merck is a huge pharmaceutical, so approval will result in a 20% appreciation in stock, and rejection in a 10% decrease. She is also considering hedging her bets and investing half her money in Merck and half in the Biotech firm. She could also put her money in a safe mutual fund, with a small (but guaranteed) 3% increase in value in the next six months.
a) Fill in the decision table, labeling all decisions, outcomes and payoffs. Express payoffs in terms of expected portfolio value at the end of six months. Hint: the table has the correct dimensions.
b) Given the payoff table what is Sheree’s best decision using the Laplace, Maximax, and Maximin decision criteria? Please show the decision, not just the payoff amount for full credit. (Merck, Biotech, Mutual Funds)
c) Sheree thinks that the chance of the FDA approving the drug is 40%. Compute the expected values for each decision, and circle her best decision, assuming she is rational and risk neutral. (all Biotech 800, Merck 1020, 50/50 910, Mutual Funds 1030) d) Construct the opportunity table below and show what investment Sheree would make under the Minimax Regret Decision Criteria (no points just for guessing!) (50/50)
DS 412/BUS 786 Final Review Sheet
Department of Decision Sciences
San Francisco State University
2. Yonni is considering expanding his Yuppie Yoga franchise by building a new studio in Russian hill that will cost 6 million dollars to build and operate (over the relevant timeframe of the model). Customer demand is uncertain, however. There is a 0.6 probability it will be high, yielding him 10 million in revenues, but if it is low he only will earn 5 million in revenues from a half-full club. If demand is low, he does have the option of trying to raise it through a marketing campaign. If successful, this raises his club's revenue's to 8 million dollars. However, the campaign will cost 2 million and only has a 50% chance of success and if unsuccessful, club revenues remain at 5 million. Also, Yonni can choose not to build (and his profit would be 0). a) Draw a decision tree to show Yonni's decision process, wherein he attempts to maximize his profits. Show all final payoffs and intermediate expected values. (Reminder: profit = revenues- costs. All costs that are relevant to the problem are mentioned explicitly!) b) Assuming Yonni is a risk-neutral, rational decision maker, what is his course of action over the timeframe of the model? (build studio, don’t advertise) c) What is the expected value of this decision tree? ($2 million) 3. Bratt's Bed and Breakfast, in a small historic New England town, must decide how to...