12-6. A very important levee spans a distance of 10 miles on the outskirts of a large metropolitan area. Hurricanes have hit this area twice in the past 20 years, so there is concern over the structural integrity of this particular levee. City engineers have proposed reinforcing and increasing the height of the levee by various designs to withstand the storm surge of numerous strength categories of hurricanes.

Study results regarding the probability that high flood water from a hurricane in any one year will exceed the increased height of the levee, and the cost of construction of the levee for each storm category, are summarized next.

Probability Capital of a Storm Surge Investment Hurricane Exceeding the to Increase the Category Levee Height Levee Height 5 0.005 $70,000,000 4 0.010 50,000,000 3 0.030 35,000,000 2 0.050 20,000,000 1 0.100 10,000,000 A panel of experts suggests that the average property damage will amount to $100,000,000 if a storm surge causes the levee to overflow. The capital investment to rebuild the levee for each hurricane category will be financed with 30-year municipal bonds earning 6% per year. These bonds will be retired as annuity payments each year. What is the most economical way to rebuild the levee to protect the city from flooding during a hurricane? What other factors might affect the decision in this situation?What if the average damage from a flood is $200,000,000? (12.4)