Problem 4 (30) Given: You are tasked with evaluating three possible foundation design alternatives for a new bridge considering extreme flood limit state, possible damage, and repair cost, and a 75-year design service life. The occurrence of an Extreme Flood Event is Poisson-distributed with mean arrival rate of = .002/year, and therefore, the probably of an extreme flood event occurring within 75 years is 0.14. Associated costs and conditional probabilities are listed in the following table. Foundation Initial Probability Type construction (DamageExtreme Repair Cost Damage & cost Flood) P(Cost|Damage) P=0.2 P=0.5 P=0.3 Shallow $2.0M .4 SIOM $20M $30M Footing Driven Piles $3.0M .3 S2M $3M S6M Drilled Shaft $4.0M .1 $3M $4M $8M Using Decision-Tree Analysis Method: a.) Construct the decision tree model representing the decision (10) b.) Determine expected cost for each foundation decision. (10) c.) Determine the expected cost of perfect information. (5) d.) Rank each foundation type according to expected cost criteria from lowest to highest