# Which dam height minimizes the expected total annual cost?

Generate Analytica models for the following two questions and upload your models (.ana)

Question 1

A dam is being considered to reduce river flooding resulting from climate change. But if a dam is built, what height should it be? Increasing the dam’s height will reduce a flood’s probability and the damage when floods occur, but increase construction and maintenance costs. Which dam height minimizes the expected total annual cost? Note that the state uses an interest rate of 7% for flood protection projects, and all the dams should last 60 years.

 Dam height Construction cost Annual Maintenance cost Annual Prob(flood>height) Damage if flood occurs No dam \$0 \$0/year 0.40 \$1,000,000 10 ft \$400,000 \$2,000/year 0.20 \$900,000 20 ft \$500,000 \$4,000/year 0.10 \$800,000 30 ft \$600,000 \$6,000/year 0.05 \$700,000 40 ft \$700,000 \$8,000/year 0.01 \$600,000 50 ft \$800,000 \$10,000/year 0.001 \$500,000

Question 2

A community near the ocean is suffering from drinking water scarcity due to climate change. The community plans to build a water desalination system to transform seawater into fresh water. Once its useful life is over, the system will be sold at salvage value. Considering the following conditions, what is the rate of return?

Uniform annual benefit: \$80,000 per year

Initial cost: triangularly distributed with a min of \$500,000, a mode of \$700,000, and a max of \$1,000,000

Salvage value: normally distributed with a mean of \$60,000 and a standard deviation of \$9,000

Useful life: uniformly distributed over 10 to 15 years

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