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Assume that a vaccine expires in one month. The monthly demand for the vaccine has a normal distribution with the mean of 200 and the standard deviation of 30. The vaccine cost is $15/unit and the penalty to the medical center for getting short of vaccine is $80 per unit. What is the optimum quantity of the vaccine to purchase for a month? (The medical center does not earn any profit on vaccines.)

[Provide single value answer. Maintain 3 decimal places.]