Question: A certain port authority has decided that it needs to deepen its harbour so that larger ships can use the port. The bottom of the harbour appears to consist of deep sand meaning that the job can be done using dredges at a cost of $60000. However, some of the older residents claimed that there are boulders underthe sand that will damage the dredges. If this is true then an attemative method of excavation will be required involving that the harbour be closed with a cotterdam and the water removed so that normal earthmoving equipment will be able to excavate the (now dry) bottom of the harbour. This will cost $260000. If dredging equipment is used when boulders are present then the both costs will need to be paid for a total of $320000. The port authority has commissioned some consultants to investigate and they believe that the probability that boulders are present is 0.5. These consultants have suggested that more testing occur. Two types of testing are available. Minor testing and major testing. They claim that minor testing will have a probability of 0.2 of a positive test result indicating that boulders are present. If minor testing gives a negative test result then the probability that boulders are present drops to 0.375. This testing will cost $20000. They claim that major testing will have a probability of 0.4 of a positive test result indicating that boulders are present. If major testing gives a negative test result then the probability that boulders are present drops to 0.16666667. This testing will cost $30000. A maximum of one type of testing should be used. If testing gives a positive test result then a cofferdam will be built. It the result is negative then the port authority still needs to decide what to do because it is no guarantee that no boulders are present. The port authority is committed to deepening the harbour. It is just a question of which method to use and what testing, if any, should be performed beforehand. Create a decision tree below to represent this situation and determine what the port authority should do using the EMV criterion. In the case of decisions please use probability = 1 for options that are chosen and probability = Dior options that are rejected. Monetary values should be answered to the nearest dollar. Probabilities should be answered to three decimal places. 00 not include dollar signs or commas.

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