The pharmaceutical company NovoMed has given funding to two research teams, one at Harvard and one at Stanford. The ultimate goal of each team is to develop experimental drugs, in an attempt to improve the effectiveness of NovoMed's current drug for treating diabetes. The results from randomized trials of the drugs developed by Harvard are becoming available in the next year, with Stanford following in the year after that. After the results of these trials are released, the effectiveness of the corresponding drugs will be exactly known. The effectiveness of each technology is represented by a score: 1, 3 or 4. An effectiveness score of 1 means that the drug has no significant improvement over the current drug for treating diabetes. A score of 3 means that the drug has a significant improvement over the current drug, and NovoMed believes they can sell the drug. An effectiveness score of 4 means that the drug could become the new "gold standard" for treatment. NovoMed expects the results to have the distribution specified in the following table. For example, NovoMed believes that the probability that Harvard's drug yields a score of 1 is 0.7. Due to an agreement on intellectual property reached between NovoMed and the research teams, when the trials' results for each drug become available, NovoMed has to choose from one of the following decisions: i. NovoMed rejects the drug. In this case, the related research findings for that particular drug will be published in the public domain, and it is unlikely that NovoMed will be able to turn the drug into production in the future. ii. NovoMed accepts the drug. This means that NovoMed will take the drug to the next phase of the development process, commit all its resources to developing the chosen technology, and no longer wait for other related clinical trial results. If, by the end of the second year, NovoMed decides to reject both drugs, then it will be forced to pursue its current existing drug, which has an effectiveness score of 2. Probability Score Team at Harvard Team at Stanford 1 0.7 0.8 3 0.3 0 4 0 0.2 1. Construct a decision tree and find the optimal strategy that maximizes the expected effectiveness score of NovoMed's choice. What is NovoMed's maximum expected score under this optimal strategy? (Briefly describe your strategy in words, and clearly indicate each branch of the tree that your optimal decision strategy would choose.) 2. (25 points) How does your optimal decision strategy change if the probabilities of the various scores change? Please clearly state values at which the optimal decision strategy changes