Don't answer it if you do not show the detail of the formula and the calculation. Please show the details.

1. The annual demand for a product is 4,160 units per year (assume 52 weeks in a year). The weekly demand is 80 units with a standard deviation of 5 units. The cost to place an order is $128, and the lead time from ordering to receipt is 3 weeks. The annual inventory carrying cost is $2.6 per unit. The operations manager needs to decide which inventory control policy to use.

a) Option 1: EOQ model with safety stock. How much safety stock should be kept in order to make stockout occur with no more than 5% chance? What is the corresponding reorder point and the optimal order quantity?

b) Option 2: Fixed-time period model with safety stock. Suppose the manager plans to order every 8 weeks. There are 260 units inventory on hand. How much safety stock and how many units should he order to have no more than 5% chance of stockout?

c) Compare the safety stock levels and the order quantities calculated in parts a) and b). What observation can you make with regard to the average inventory using these two inventory control policies? (Word limit: 50)