(50 points) The inventory of an item is controlled with a continuous review (Q,R) policy. The fixed ordering cost is $100, the unit purchase cost is $5, the inventory holding cost per unit per year is 20% of the unit purchase cost, and the expected annual demand is 10000 units. The lead time demand is normally distributed with a mean of 400 and a standard deviation of 30. All shortages are backordered at a cost of $3 per unit. (a) (10 points) Find the reorder point that minimizes the expected annual cost if a lot size of 900 is to be used. Calculate the expected annual cost in this case. (b) (10 points) Find the lot size that minimizes the expected annual cost if a reorder point of 400 is to be used. Calculate the expected annual cost in this case. (c) (15 points) Find the optimal values of the lot size and the reorder point. Perform at most three iterations (including iteration 0). Calculate the optimal expected annual cost. (d) (15 points) Now ignore the shortage cost. Find the optimal values of the lot size and the reorder point when a Type 1 service level of 0.95 is required. Also, find the optimal values of the lot size and the reorder point when a Type 2 service level of 0.95 is required. Perform at most three iterations (including iteration 0). (50 points) The inventory of an item is controlled with a continuous review (Q,R) policy. The fixed ordering cost is $100, the unit purchase cost is $5, the inventory holding cost per unit per year is 20% of the unit purchase cost, and the expected annual demand is 10000 units. The lead time demand is normally distributed with a mean of 400 and a standard deviation of 30. All shortages are backordered at a cost of $3 per unit. (a) (10 points) Find the reorder point that minimizes the expected annual cost if a lot size of 900 is to be used. Calculate the expected annual cost in this case. (b) (10 points) Find the lot size that minimizes the expected annual cost if a reorder point of 400 is to be used. Calculate the expected annual cost in this case. (c) (15 points) Find the optimal values of the lot size and the reorder point. Perform at most three iterations (including iteration 0). Calculate the optimal expected annual cost. (d) (15 points) Now ignore the shortage cost. Find the optimal values of the lot size and the reorder point when a Type 1 service level of 0.95 is required. Also, find the optimal values of the lot size and the reorder point when a Type 2 service level of 0.95 is required. Perform at most three iterations (including iteration 0)