Solar C is the coffee shop located at the 1st floor of SolBridge building. Solar C uses 28 bags of roasted coffee bean per week on average. The weekly usage is random and can be estimated as Normal distribution with standard deviation of 3.8 bags per week. Solar C orders coffee bean from a supplier with 2 weeks of lead time, and there will be shipping cost $50 for each order. The new manager desires a chance of stockout of 5% or lower. and estimates the annual inventory holding cost is 25% of the purchasing price, $10 per bag. Assume 1 year = 50 weeks. a) (10 points) Using EOQ, find out the order quantity. Because Solar C will use an integer value, please round the answer to the nearest integer. b) (10 points) At what level of inventory does Solar C have to place an order to maintain the stockout probability Of 5% or lower? (ROP) c) (15 points) Suppose the manager is using the ROP described in part b). One day, the manager tried to place an order, since the inventory level hit the ROP, to the supplier and heard that the supplier could not ship out the coffee bean for a week due because the coffee roast machine is under maintenance. It meant the order would take one more week to arrive this time. After hanging up, the manager thought about purchasing coffee bean somewhere else. But before making the decision, she wanted to know the stock out probability. Assuming the suppliers promise is valid, what is the probability that Solar C would run out of coffee bean before the shipment arrives? (round to the nearest hundredth, for z value or use Excel function) d) (15 points) Solar C changed the ordering policy to periodic review a few months ago. Now, SolBridge places an order every 4 weeks. The desired stockout probability is still 5%. Today is the order day. Before SolBridge places an order, the manager confirms that it has 15 bags in the storage. How many begs should Solar C order today?