A retailer uses lot-size-reorder point policy to make replenishment decisions for a brand of shampoo. Shampoo is delivered from the distribution center of the supplier three weeks after it is ordered. A bottle of it costs the retailer $4. Fixed costs of ordering amount to $200 for bookkeeping expenses, and holding costs are based on 20 percent annual rate. The retailer estimates that the loss of customer goodwill for not being able to serve the shampoo when requested amounts to $8. Based on past experience, the three-weekly demand for the bottles of shampoo is considered to be uniformly distributed between 50 and 90. For the purposes of your calculations, you may assume that there are 52 weeks in a year and that all excess demand is back-ordered. a) Determine the optimal reorder point (R) and reorder quantity (Q) that will minimize the retailer's expected average annual cost of inventory holding, setup and shortages (Perform at most 3 iterations including iteration 0). b) If the retailer chooses to order 800 bottles at each replenishment, what should be the reorder point to minimize expected annual average cost? c) What level of Type 1 service is being provided by the policy found in part (a)? d) What level of Type 2 service is being provided by the policy found in part (b)?