Bankers Training Academy (BTA) offers many different courses in a big cosmopolitan city. Most of the residents in the city are fully vaccinated after getting two doses of vaccines. Life in the region was about to become normal. But due to the COVID-19 variant, Omicron uncertainty cloud arises, partial lockdown is implemented. BTA is planning to launch their famous risk management certification program. Before pandemic, they only conducted in-person mode of delivery, where students must come to the campus to attend the meetings. Since the pandemic started, BTA only performed remote methods of delivery. This teaching model became very famous due to the flexibility of synchronous and asynchronous teaching with recorded lectures. Candidates interested in the certification are divided into two groups for the upcoming season. One group is interested in an in-person mode of delivery. whereas the other group is interested if offered remotely. BTA management has to decide to launch or not launch the certification program first. If they decide to launch, then they have to determine the mode of delivery between "In-person," "Remote," or "Both" (in-person and remote). From the previous experience, BTA management believed that if the mode of delivery is in-person, then there will be high enrolment with 42% probability and low with 58% probability. However, if the certification program launches remotely, the administration estimates that the enrollment in the program will be high with a 35% probability and low with 65%. The BTA administration is sure of these probabilities and does not feel like they need a further survey to learn more about them. On the other side, if the mode of delivery is (in-class and remote) "Both," there will be high enrolment with 62% probability and low with 38% probability. However, before making the launching "Both" mode of delivery, the director of the BTA has to decide whether or not to carry out a survey that costs $8500. The survey will indicate that the possible demand for the program will be high or low with respective probabilities of 85% and 15%. If the director decides to carry out the survey, the director will still decide whether to launch the certification program in light of the survey result. Based on the result of the survey, if the director decides to launch the program, the probabilities of the actual enrolment in the program are given as follows: If the survey indicates a High Demand and the program is launched. In that case, it is believed that the actual enrollment will be high with a probability of 78%, moderate with a probability of However, before making the launching "Both" mode of delivery, the director of the BTA has to decide whether or not to carry out a survey that costs $8500. The survey will indicate that the possible demand for the program will be high or low with respective probabilities of 85% and 15%. If the director decides to carry out the survey, the director will still decide whether to launch the certification program in light of the survey result. Based on the result of the survey, if the director decides to launch the program, the probabilities of the actual enrolment in the program are given as follows: If the survey indicates a High Demand and the program is launched. In that case, it is believed that the actual enrollment will be high with a probability of 78%, moderate with a probability of 15%, and low with a probability of 7%. If the survey indicates a Low Demand and the program is launched, it is believed that the actual enrollment will be high with a probability of 26% and low with a probability of 74%. Launching the certification program with an "in-person" mode of delivery will cost $61720, "remote" method of delivery will cost $46800, whereas if "Both" mode of delivery is decided, then it will cost $96400. Furthermore, remote launching needs to upgrade the IT system that needs an additional $15500 (not required at all if the mode of delivery is only in-person.) It is estimated that: high enrollment will bring in a revenue of $240800; moderate enrollment will bring in a revenue of $155800, and low enrollment will generate a revenue of $65750. (a) Construct a decision tree to represent the BTAS' problem; state/calculate all probabilities, payoffs and EMV'S. (b) Assuming that the BTA wants to maximize expected profit (i.e., revenue-costs), solve the tree and state the complete optimal strategy. What will be their expected profit? (Show your work. Otherwise, you will not get marks even the answer is correct!) (c) Does the given problem pass the clarity test? Please state your answer as yes or no, and then justify your answer to get full marks