3.15 Hurricane Hillary recently made landfall on the East Coast of the United States, causing extensive damage to many of the health care facilities in the Chesapeake region of Virginia. Metts Community Hospital was hit particularly hard, accruing over $3 million in water damage alone. The hospital is focusing its initial efforts on repairing the water damage in the intensive care unit. The hospital's administrative resident has put together three options for consideration to repair the water damage in the intensive care unit: (1) full renovation, (2) major structural renovation, and (3) minor renovation. The damage needs to be repaired within the next three months. However, hurricane season continues throughout the repair period, and the weather conditions could affect the costs of the repairs. Fair weather has a probability of 0.35, mild weather has a probability of 0.25, and inclement weather has a probability of 0.40. In the event of fair weather, option (1) will cost $400,000, option (2) will cost $250,000, and option (3) will cost $175,000. In the event of mild weather, option (1) will cost $425,000, (2) will cost $285,000, and (3) will cost $210,000. In the event of inclement weather, option (1) will cost $500,000, (2) will cost $325,000, and (3) will cost $275,000. a. Construct a payoff table of the hospital's three alternatives for each weather condition. b. Develop a decision tree for this problem. Be sure to show cost outcomes, probabilities, and the expected monetary value for each event node. c. Analyzing this problem using the decision tree format, which repair alternative should be chosen? d. Calculate and interpret the expected value of perfect information.