$1.$ Petromax Enterprises uses a continuous review inventory control system for one of its SKUs. The following information is available on the item. The firm operates $50$ weeks a year. Demand $=50,000$ units$/$year Ordering cost $=$ $$35/$order Holding cost $=$ $$2/$unit$/$year Average lead time $=3$ weeks Standard deviation of weekly demand $=125$ units a$)$ What is the economic order quantity for this item? b$)$ If Petromax wants to provide a $90$ percent cycle$-$service level, what should be the safety stock and the reorder point?