While working at the mine, a fatal influenza pandemic has created panic in Ossian's home country. This outbreak was not totally unexpected, since a neighboring country experi- enced a similar outbreak last year. Last year, the Red Cross got the pharmaceutical company Profitera to agree to provide doses of a vaccine in anticipation of this year's season.

The process of providing vaccines involves forecasting demand far ahead of an outbreak, since doses of a vaccine take months to produce. If there is a large outbreak, there is insufficient time to quickly produce more vaccine to meet the need. Profitera estimated that demand for doses of the vaccine this year would be normally distributed with a mean of 1 million doses and a standard deviation of 300,000 doses.

In making a decision on how many doses to supply, Profitera executives felt the only downside cost of not supplying enough doses would be bad PR in the North American press. They esti- mated this cost to be 1 dollar per person who needed the vaccine but could not get one. Each dose cost Profitera 2 dollars to produce and ship to Ossian's home country. Unused vaccines spoil and must be written off at 100 per cent of the cost of production.

(a) Based on Profitera's cost estimates, what is their optimum service level for doses of influenza vaccine supplied to Ossian's home country?

(b) Based on this service level and using the appropriate model from class, how many doses should Profitera ship to Ossian's home country?