1) You are considering opening an independent gas station with a convenience store. Your problem is that you are not sure how large of a gas station to open. The level of profitability will depend on gasoline company advertising, demand for gasoline, and the size of the gas station. After investigating the market and prospects for the next year you have concluded that the following payoff table reflect the expectations for the next year.

Size of Station

Good Market

Fair Market

Poor Market

Small

50,000

20,000

-10,000

Medium

80,000

30,000

-20,000

Large

100,000

30,000

-40,000

Very Large

300,000

25,000

-100,000

a) What is the optimistic (maximax) decision?

b) What is the pessimistic (maximin) decision?

c) What is the equally likely (LaPlace) decision?

d) What decision would you make using the criteria of realism (Hurwicz)? Assume that the a value is 0.8.

e) Using minimax regret (Opportunity Loss Regret) what size gas station should you open?

2) Farm Grown sells boxes of vegetables and other farm products. Each case costs $5 and sells for $15. Any boxes left over for the day are sold to a food processing company that pays $3 per box. Farm Grown also has a policy of satisfying customers. If a customer wants a box and Farm Grown does not have any boxes they will buy it from a competitor for $16. Farm Grown has determined that there is a 30% chance that they will sell 100 boxes, a 40% chance they will sell 200 boxes, and a 30% chance they will sell 300 boxes.

This means that the relevant profit equation is

Where

Q = the number of boxes that Fam Grown sells to customers

X = the number of boxes that Farm Grown buys for itself

Y = the number of boxes that they must buy from competitors

Z = the number of boxes sold to the food processing company.

For example, if Farm grown buys 300 boxes of vegetables and then sells 100 boxes their profit for the day would be

If Farm Grown buys 100 boxes of vegetables and other farm products but they have sales of 200 boxes their profit would be

Farm Grown must decide how many boxes of vegetables and other farm products they will need to buy.

a) Using the expected value (EV, EMV) approach how many boxes of vegetables and other farm products should Farm Grown buy?

b) Using the expected opportunity loss criteria how many boxes of vegetables and other farm products should Farm Grown purchase?

3) Beverly Mills has decided to lease a hybrid car to reduce her driving expenses and to lower greenhouse emissions. After considerable investigation she has decided on the vehicle to lease but is not sure which lease contract to take. All three of her options are for three-year leases. The first option has a monthly base cost of $330 a month, an allowance of 36,000 miles (12,000 per year), and an extra mileage fee of $0.35 per mile. The second option has a fee of $380 a month, an allowance of 45,000 miles, and an extra mileage fee of $0.25 per mile. The third option has a monthly fee of $430 a month, a mileage allowance of 54,000, and an extra mileage fee of $0.15 per mile. Beverly has estimated that there is a 40% chance she will use her car 12,000 miles per year, a 30% chance that she will drive 15,000 miles a year, and a 30% chance she will drive 18,000 miles a year during the lease. Beverly would like to keep her costs as low as possible and has asked you of you could help make the decision. The relevant equation for Beverly costs is

For example, if Beverly chooses option 2 and drives 18,000 miles per year her cost will be

If Beverly chooses option 2 and drives for only 12,000 miles a year her cost will be

a) Using the optimistic criteria which lease should Beverly select?

b) Using the pessimistic criteria which lease should Beverly select?

c) Using the expected value approach which lease should Beverly select?

d) What is the value of perfect information for Beverly?