Please answer clearly with all calculations

Answer the following questions in the space provided. Please show your work. Under the periodic review system, stock is ordered at predetermined times. The rule is to order up to restocking level taking into account the inventory on hand when the order is placed. (Q=R-I) The equation for the restocking level (R) is: R = MRP+L + 20 RP+L 1. Calculate the order to replenish inventory under each of the following conditions: a. mean demand during the reorder period and the order lead time is 125 units, the standard deviation of demand during the reorder period and the order lead time is 36 units, and the desired level of service is 75% R= If the current inventory is 52 units, what is Q? Q= b. mean demand is 50 units per day, orders are placed every 14 days, the lead time is 3 days, the standard deviation of demand is 5 units per day, and the desired level of service is 90% R= If the current inventory is 172 units, what is Q? Q= c. mean demand is 240 units per day, orders are placed every 7 days, the lead time is 1 day, the standard deviation of demand is 20 units per day, and the desired level of service is 95% R= If the current inventory is 215 units, what is Q? Q= Under the continuous review system, inventory is monitored continuously and an order is placed when inventory falls below the reorder point. Q = 2DS = EOQ H 2. Calculate the economic order quantity for the following: a. annual demand is 1500 units, annual holding cost is 42 AED per unit and order cost is 150 AED EOQ = b. annual demand is 5000 units, annual holding cost is 510 AED and order cost is 1000 AED EOQ = Safety stock is stock held in case of above average demand during the lead time for a continuous review system or an unexpected delay in receiving an order. The equation for calculating safety stock is: zVog tao? Safe stock = 3. Calculate the desired level of safety stock for each of the following situations: a. average lead time is 4 days, average demand is 35 units per day, variance of demand is 9 units per day, variance of lead time is 1 day, the desired level of service is 99% b. average lead time is 2 days, average demand is 20 units per day, standard deviation of demand is 5 units per day, standard deviation of lead time is 0.5 days, the desired level of service is 80% Under the continuous review system, the reorder point is calculated as: d + zVos doi + 4. Calculate the reorder point under the following conditions: a. mean demand is 60 units per day, mean lead time for an order is 2 days, and the safety stock is 145 units. R= b. mean demand is 25 units per day with a standard deviation of 10 units, mean lead time is 2 days with a standard deviation of 2 days and the desired level of service is 90% R= + DP 5. A quantity discount is available to a company. The total cost of inventory for a year is: Total holding, ordering, and item costs for the year = ()++ @)s : a. Calculate the EOQ under the following conditions: annual demand is 1000 units, annual holding cost is 45 AED per unit and order cost is 100 AED b. Calculate the total cost of inventory for a year at the EOQ if the unit cost is 250 AED c. The following quantity discount levels are available. Which, if any, of the quantity discounts should the company take advantage of? Show your work. 1-25 units = 300 AED 26-50 units = 250 AED 51-100 units = 210 AED 101 units plus =200 AED