A County is considering whether to build a levee along the river bank as a flood control system. The two alternative solutions are:
1- A 5-foot high levee costing $ 10000000, and
2- a 10-foot high levee costing $25000000
Both levees would have a useful life of 100 years. Historical records indicates that there is a 10% chance that the river will rise between 2 ft and 10ft, and a 2% chance that it will rise over 10ft. Any flood caused by river rising more than 2 ft in the absence of a levee or overflowing the levee is estimated to cause $ 200000000 in property damage.
A- Which option has the least expected cost? Note: having no levee is also for consideration.
B- Property damage in monetary term is not the only criterion for decision making. Suppose this county could consider the utility of property damage as a function of the pay-off cost as indicated in the equation below , what should its decision be ?
Utility function: U=1- (1/50625)*Xˆ2
Where X is the pay – off cost to the County.
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