Decision Tree Homework Problem The Blossom River is tidal in its lower reaches. This means the elevation of the water in the river is determined both by tides and by run-off associated with precipitation. There has been increased seasonal flooding frequency in the river, which has been determined to result from higher spring tides (associated with global warming impacts) and greater run-off amounts, due to increases in impervious surfaces in the river watershed (more paving in the upland areas). The Army Corps of Engineers is constructing a tidal barrier at the mouth of the river. However, it will take two years to complete the project. The ACOE needs to design a temporary solution to the current flooding problem. Note that each flooding episode results in federal compensation payouts of $20 million. ACOE can do nothing, relying on the natural banks to prevent impacts from a flood stage of 9.5 feet or less. ACOE can build a cheap, temporary barrier at a cost of $9 million to a flood stage height of 11 feet. If a flood exceeds that height in the first season, there is a 30% probability that the temporary barrier will be substantially destroyed. Repairing the barrier to be effective for the second flood season would cost $7 million. ACOE can build a more substantial barrier that will not be damaged even if the flood stage exceeds its height. The footing of the barrier would cost $4 million, with each additional foot in height costing $1 million. For obscure technical reasons, this barrier can only be either 11 or 13 feet tall. The probability in any one year of a 9.5 feet or higher flood is 37%. The probability of a flood in any one year exceeding 11 feet is 9%. The probability of a 13 feet or higher flood in any one year is 0.4%. a) Draw the decision tree for this problem. b) assuming no time cost for money, and assuming ACOE wants to minimize its costs, select a course of action (and justify your answer).