Aventis is a major manufacturer of the flu (influenza) vaccine in the U.S. Because of capacity constraints, Aventis manufactures the vaccine before the flu season at a cost of $6 per dose (a ‘dose’ is vaccine for one person). During the flu season Aventis sells each dose to health-care providers for $24. However, sometimes the flu season is mild and not all doses are sold – if a dose is not sold during the season then it is worthless and must be thrown out. Before the 2003-04 flu season, Aventis’ forecast of demand for its vaccine was a normal distribution with a mean of 40 million doses and a standard deviation of 12 million. a) Find the profit-maximizing number of doses manufactured by Aventis. In 2004, the U.S. ran out of flu vaccine. To improve public health, the U.S. Department of Health is considering incentives to Aventis to encourage higher levels of production. In particular, the department would like Aventis to make enough vaccine so that the probability of running out in a particular season is 10%. One possible incentive is to purchase all unused doses of vaccine (a ‘buy-back’ program). For example, if Aventis manufactures 50 million doses and sells 40 million, the government would buy back each of the remaining 10 million for some price. b) What price per unit must the government offer for each unused dose so that Aventis meets the ‘10%’ goal? Another possible incentive is a ‘price support’ program – the government would pay extra money for each dose sold. For example, if Aventis sells 40 million doses, the government would pay Aventis a bonus for each of the 40 million. c) What bonus per dose sold must the government offer so that Aventis meets the ‘10%’ goal? d) Compute the expected cost to the government for each program. You may want to use the tables below, which show the expected number of doses sold by the end of the season, given various possible manufacturing quantities. Cost of buy-back program: $ _____________________ Cost of price support program: $ ___________________ Calculations: