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A hospital needs 3,000 units of a medicine throughout the year. The purchasing cost varies with the size of the order. If the number of units of the medicine that the hospital orders is below 100, the supplier charges $30 per unit; if it is between 100 and 499, the price is $27 each; and if they order 500 units and above, it is $26 per unit. The holding cost per unit per year is $30, as the medicine must be kept in a special device to prevent spoilage. The ordering cost is $10.
a. How many units of the medicine can hospital order each time to minimize their total cost? (Round your answer to a whole number.)
b. What is the minimum annual total cost? (Round your answer to a whole number.)
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