Office Supply Company (OSC) has a spare parts warehouse in Alaska to support its office equipment maintenance needs. Once every six months, a major replenishment shipment is received. If the inventory of any given part runs out before the next replenishment, then emergency air shipments are used to resupply the part as needed. Orders are placed on January 15 and June 15, and orders are received on February 15 and July 15, respectively. OSC must determine replenishment quantities for its spare parts. As an example, historical data show that total demand for part 1AA-66 over a six-month interval is Poisson with mean 6.5. The cost of inventorying the unneeded part for six months is $5 (which includes both physical and financial holding costs and is charged based on inventory at the end of the six-month period). The variable production cost for 1AA-66 is $37 per part. The cost of a regular, semiannual shipment is $32 per part, and the cost of an emergency shipment is $50 per part. It is January 15 and there are currently three 1AA-66 parts in inventory. How many parts should arrive on February 15?
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