A manufacturing company has a production facility in Miami, FL. This facility can generate a regular profit of $10 million annually. The threat of hurricane is always an issue for this facility. It is estimated that a strong hurricane (category 3 or higher) can cause a damage of around $20 million. The company has the option of buying an insurance policy that covers 80% of this potential damage. The cost of this type of policy is $3.5 million. This policy should be bought at least 6 months before the hurricane season. The average probability of occurrence of a strong hurricane in that region is estimated to be 50%. The company also has the option of waiting until the beginning of the hurricane season to buy the insurance policy with a higher price of $4 million. At the beginning of the season, the weather forecast indicates that either this is a high risk season or a low risk season. A high risk season happens with a probability of 50% and during such a high risk season, a strong hurricane happens with a probability of 90%. A low risk season which happens with a probability of 50% and during such a low risk season a strong hurricane happens with a probability of 10%.

Note: the company generates its $10 million profit regardless of happening of a hurricane.

Draw a decision tree and specify: a. The best decision course; whether to make a decision 6 months before the hurricane season or to wait for the beginning of the hurricane season whether to buy an insurance policy or not

b. The expected profit/loss based on this best decision,

c. The risk profile.

Optional for extra credit (up to 10 points) d. The expected profit with perfect information (optional: extra credit) e. The expected value of perfect information (optional: extra credit)