A certain chain of sports stores is considering to change its current inventory control system to manage its inventory of bicycle and sports helmets. The information regarding the helmets are as follows: Average demand: 100 units/week Lead time = 5 weeks Order cost = $65/order Unit cost = $90 Carrying rate = 10% Standard deviation of weekly demand = 30 Desired service level = 95% (z-value = 1.645) Number of weeks per year = 52 Inventory position ([P) = 300 units a) The inventory manager is planning to use a xed-period inventory system model. Calculate the optimal time interval {T} and replenishment level 1M 1 for a xed-period inventory model with or without safety stock. Comment briey on your dings and how this system operates. (b) As the supply chain planner, do you think that the xed-period inventory system model is suitable for this store? In your answer, you need to consider the benets and challenges of three inventory models. Use your own words in your discussion.