1. A payoff table is given as 

	S1	S2	S3
D1	10	8	6
D2	14	15	2
D3	7	8	9

For 5 points each, answer the following questions: 

a. What decision should be made by the optimistic decision maker? 

b. What decision should be made by the conservative decision maker? 

c. What decision should be made under minimax regret? 

d. If the probabilities of s1, s2, and s3 are .2, .4, and .4, respectively, then what decision should be made under expected value? 

e. What is the EVPI? 

f. Draw a decision tree for this problem 

2. If sample information is obtained, the result of the sample information will be either positive or negative. No matter which result occurs, the choice to select option A or option B exists. And no matter which option is chosen, the eventual outcome will be good or poor. For 10 points complete the table. 

Sample Result	State of Nature	Prior Probability	Conditional Probabilities	Joint Probability	Posterior Probability
Positive	Good	.7	P( positive good)=.8
	poor	.3	P(positive/poor) =.10
Negative	Good	.7	P(negative/good
	Poor		P(negative/poor)

3. For 5 points each, answer the following questions concerning the forecast listed below. 

Month	1	2	3	4	5	6	7
Demand	20	25	40	30	50	58	65

a. Forecast for month 8 using the three-month moving average. What is the MSE? 

b. Forecast for month 8 using exponential smoothing with a smoothing constant of .4. What is the MSE? 

c. From the analysis performed above, which technique is most desirable? 

4. For the payoff table below, the decision maker will use P(s₁) = .15, P(s₂) = .5, and P(s₃) = .35.

	State of Nature
Decision	s1	s2	s3
d1	-5,000	1,000	10,000
d2	-15,000	-2,000	40,000

1. What alternative would be chosen according to expected value?
2. For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1- p), the decision-maker expressed the following indifference probabilities. 

Payoff	Probability
10,000	.85
1,000	.60
-2,000	.53
-5,000	.50

3. Let U(40,000)=10 and U(-15,000)=0 and find the utility value for each payoff. 

 What alternative would be chosen according to the expected utility? 

5. As part of their application for a loan to buy Sunnyside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected: Daily fixed cost (loan payment, taxes, insurance, maintenance) are $200/night. Variable cost per occupied room per night $ 25 

Revenue per occupied room per night $ 70 For 5 points each, answer the following questions: 

a. Write the expression for total cost. 

b. Write the expression for total revenue per day. 

c. If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even? 

6. Below is a list of sales. 

Year	1	2	3	4  5	6  7
Sales	20	25	30	33  39	43  51

For 5 points each, answer the following questions: 

a. Graph this time series. Does a linear trend appear? 

b. Develop the equation for the linear trend component for the time series. 

c. Use the linear trend developed in part (b) to prepare a forecast for sales in year 8.