For one particular SKU a retailer faces a demand of D ~N(160,42) per week (assume independence). Each unit of the product has a holding cost of $8/week (due to opportunity costs associated with being able to use the shelf-space to advertise another product). Setting up a new order will cost $10 (regardless of order size), and it will take one week for the order to come in. Unfulfilled demand is backlogged, and each customer facing a stockout is given a gift that costs the retailer $3. appropriate, iterate until you notice your order quantity values are not changing in the tenths place after rounding (even though realistically order quantities will be whole numbers, since we are dealing with an SKU). 1. Assuming a continuous review system, find the optimal inventory management policy. 2. Find the safety stock, type I service level, and type II service level associated with your answer in Problem 1. 3. Describe a reasonable policy that could be used under periodic review (and give approximate numerical values associated with this policy). Would such a policy be more effective under frequent reviews or infrequent reviews? 4. Assuming continuous review again, how would the inventory management policy change if lead times are variable, assuming a mean of one week and a standard deviation of 0.5 day (i.e., a variance of 1/196 weeks)? State two necessary assumptions for carrying out your analysis and give the new values associated with your policy.