3. An engineer must decide between spread footings or piles for a foundation to support each column of a building.  The soil strength is not known for certain, but could be low (?1), medium (?2), or high (?3).  Spread footings for the building have a total cost of $150,000, while piles cost $250,000.  The piles are considered “safe” in that if the actual soil strength turns out to be low, no damage will result to the building.  The spread footings are less expensive but would result in some building damage if the soil strength is low or medium, and they would have to be replaced with piles (under difficult construction conditions) if the soil strength is low.  Costs are summarized in Table 1.  For $10,000, field studies and a triaxial strength test can be conducted.  Based on 100 samples, the actual strength of the soil samples are as follows: 30 of the samples had a low strength, 40 had a medium strength, and 30 had a high strength.  The experimental results from the triaxial strength test are summarized in Table 2.  Using a decision tree, determine what the engineer should do.

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