BESTFOOD is a private label cookie manufacturer who suppliers 4 retailers with private label cookies. Each retailer has its own composition of cookie and sells it in under their own brand name. Because the compositions are different, it takes BESTFOOD two hours to clean up a production line before starting production for a different retailer. Assume that labor cost per hour across all people involved in the cleanup is $200/hour. Also, assume that BESTFOODS has 3 cookie production lines and the production of a batch happens in whichever line is available. Retailers sell cookies in cookie packs. Demand at each retailer is 200 packs per day, and standard deviation of demand is 100 packs per day. Given these setup costs at BESTFOODS, each retailer orders cookies in batches of units, where a unit in a batch is a pack of cookies. Processing time per pack after setup is 1.5 minutes. Assume retailer holding cost is $0.04/pack/day, and 8 hours per day, 5 days per week and 50 weeks per year of operation. Assume that each cookie pack has a wholesale price per unit charged by BESTFOOD, over and above the setup cost of $1/pack.

Provide the batch size ordered by each retailer in response to the setup time for orders and the lead time faced by each retailer