Suppose that it costs $3 to make one dose of the small pox vaccine. Once a dose is made, its shelf life is 90 days, after which it can no longer be used. It is desired to have, on average, 300 million doses available at any given time. (a) What is the yearly cost to implement this plan? (b) Suppose now that the shelf life of a vaccine is randomly distributed according to an Erlang distribution with a mean of 90 days and a standard deviation of 30 days. What is the yearly cost to implement this plan? (c) Suppose that a vaccine with a longer shelf life can be made, but at a greater cost. It is found that the cost to produce a vaccine with a shelf life of x days is equal to a + bx?, where a = $2.50 and b = $0.00005. What is the shelf life that minimizes the yearly cost? =