Fleming Accessories produces paper slicers used in offices and in art stores. The mini slicer has been one of its most popular items: annual demand is 6750 units. Kristen Flemming, owner of the firm produces the mini slicers in batch. On average, Kristen can manufacture 125 mini slicers per day. Demand during the production process is 30 per day. The setup cost for the equipment necessary to produce the min slicers is $150. Carrying costs are $1 per min slicer per year.

 (1)How many minislicers should Kristen manufacture in each batch? 

(2)How long is the production cycle in each batch? 

(3)If the lead time for each batch production is 2 days, what is the re-production point, that is, at what inventory level should the next batch production be started? 

(4)If the annual demand is 8500, 6,500, 6000, 7500, 8000 units with the probabilities being 0.1, 0.2, 0.4, 0.2, 0.1, and the service level is 95%, the lead time for each batch production is 2 days, what are the safety stock and re-production point?