A soft-drink company produces 100,000 12-ounce bottles of soda per year.
By adjusting a dial, the company can set the mean number of ounces placed in a bottle.
Regardless of the mean, the standard deviation of the number of ounces in a bottle is 0.05 ounce. The soda costs 5 cents per ounce. Any bottle weighing less than 12 ounces will incur a $10 fine for being underweight. Determine a setting for the mean number of ounces per bottle of soda that minimizes the expected cost per year of producing soda.
Your answer should be accurate within 0.001 ounce. Does the number of bottles produced per year influence your answer?