Jacob is considering buying a new van for his small logistics firm. The economy in town seems to be growing, and he is wondering whether he should opt for a small, medium, or large van. The larger van would have greater capacity but will result in increased fuel consumption. A friend at the U.S. Bureau of Economic Analysis told him that there is a 25% chance of lower gas prices in his area this year, a 30% chance of higher gas prices, and a 45% chance that gas prices will stay roughly unchanged. Based on this information, Jacob has developed a decision table that indicates the profit amount he would end up with after a year for each combination of van sizes and gas prices.
Construct a decision tree and answer the following questions:
1. What is the EMV of each decision alternative?
2. Which action should be selected?
3. What is the expected value with perfect information?
4. What is the expected value of perfect information?