Question

2. (30%) Following table shows the annual damage and annual costs for a dike function of return period. Determine the return period (T) for the dike system as a system that maximizes the annual expected benefit. Т (уг) 500 200 50 100 20 10 5 0.21 0.08 0.65 0.39 1.17 1.64 Annual damage 1.94 (SM/yr) 2.3 1.9 1.4 1.0 0.2 0.6 Annual cost (SM/yr)

Answer 1

For maximum annual expected benefit, the sum of annual damage and annual costs of  dike should be minimum

for T= 5 year, the sum of annual damage and annual costs =1.94+0 = 1.94

for T= 10 year, the sum of annual damage and annual costs =1.64+0.2 =1.84

for T= 20 year, the sum of annual damage and annual costs =1.17+0.6=1.77

for T= 50 year, the sum of annual damage and annual costs = 0.65+1.0=1.65

for T= 100 year, the sum of annual damage and annual costs =1.4+0.39=1.79

for T= 200 year, the sum of annual damage and annual costs =0.21+1.9=2.11

for T= 500 year, the sum of annual damage and annual costs =0.08+2.3= 2.38

hence for T= 50 year, the sum of annual damage and annual costs =1.65 $M/yr is minimum andthe maximum expected annual benefit are for T=50 year.