Mountain Inc. produces lip-balm, the demand of lip-balm is independent. Currently, the company is following Make-to-stock policy with stable production, with forecasted demand rate of 500 units per week. The suppliers charge Mountain Inc. $0.3 for each unit, while the cost of placing a purchase order is $10. To keep a lip-balm in inventory, it costs the company 25% value of a lip-balm each year.

A. If company orders 5000 units when no more stock on hand, what is total cost each year including material cost?

B. How many lip-balms that company should order each time and how often they should order (expressed in weeks) to minimize its total cost? What the annual total cost if company follow this order policy?

C. The company observes that the demand for lip-balm is not deterministic but varies uncertainly. It is found that the demand during lead time has an average of 100 units and variance of 12. How much units should Mountain Inc. keep in safety stock to ensure 99% service level? What should reorder point be?

D. A retailer of Mountain Inc. follows continuous review system of inventory control. Demand rate of this retailer is 125 units/week, standard deviation of 15 units, lead time is 4 weeks, desired service level is 90%. Holding cost is 10$, ordering cost is 50$. Compute EOQ and safety stock?