3. If the supplier produces at the profit-optimizing Q, what is the probability that there will be an unacceptable shortfall (defined as demand being 10 million or more greater than Q). Create a graph that shows the trade-off between Q and shortfall probability. The national disease control authority has hired your team to help manage influenza (flu) vaccine production. Key facts: The problem is serious. Even in a year without vaccine shortages, ~36,000 deaths, 200,000 hospitalizations, $20 billion productivity loss. Demand for flu vaccinations is expected to be 100 million. Actual nationwide demand is uncertain, but can be approximated with a normal distribution with mean p = 100 million and standard deviation o = 10 million. A shortfall in vaccine supply exceeding 10 million doses is considered be unacceptable. One of the critical goals of the national vaccination policy is to ensure that the probability of such shortfall does not exceed 5%. Each year a new virus is targeted, so the vaccine formulation from one year cannot be used the following year. At end of each flu season, all unused vaccines need to be discarded. Economics of vaccine manufacturing: