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Week 5 Homework Assignment1. A wholesale distributor stocks and sells low flow toilets to contractors for use in commercialoffice buildings. The estimated annual demand for the toilets is 10,140 units. The estimatedaverage demand per day is 39 units. The purchase cost from the toilet manufacturer is$125.00 per unit. The lead time for a new order is 5 days. The ordering cost is $100.00 perorder. The average holding cost per unit per year is $3.75. The distributor has traditionallyordered 390 units each time they placed an order. Based upon using the distributorâs currentordering model:a. What is the average number of units in inventory based upon ordering 400 units eachtime an order is placed?b. How many orders per year will be necessary based upon ordering 400 units each timean order is placed?c. What is the average dollar value of inventory based upon ordering 400 units eachtime an order is placed?d. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) basedupon ordering 400 units each time an order is placed?e. What is the optimal reorder point based upon ordering 400 units each time an order isplaced?2. The wholesale distributorâs manager has recently heard about the EOQ model and isinterested in learning whether or not using this model would allow the company to reduce itsannual costs by optimizing the number of orders placed each year and the number of toiletspurchased in each order. The estimated annual demand for the toilets, estimated averagedemand per day, purchase cost from the toilet manufacturer per unit, lead time for a neworder, ordering cost per order and average holding cost per unit per year remain the same asstated in the scenario for the current ordering model. Based upon using the EOQ model(with instantaneous receipt):a. What is the economic order quantity (EOQ) that will minimize inventory costs?b. How many orders per year will be necessary based upon using the EOQ?c. What is the average number of units in inventory based upon ordering using theEOQ?d. What is the average dollar value of inventory based upon ordering using the EOQ?e. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) basedupon using the EOQ?f. What is the optimal reorder point based upon using the EOQ?3. The wholesale distributor has traditionally relied upon an instantaneous receipt model inwhich the material associated with each order is received in a single batch. The toiletmanufacturer has suggested that the distributor might want to consider agreeing to acceptreceipt of ordered material incrementally over a period of time rather than in a single batch asa means for reducing total annual costs. The toilet manufacturer has advised that hisfactoryâs daily production rate is 40 toilets, the duration of each production is 30 days, andthe set-up cost for each production run is $2,000. The estimated annual demand for thetoilets, estimated average demand per day, purchase cost from the toilet manufacturer per1unit, lead time for a new order, ordering cost per order and average holding cost per unit peryear remain the same as stated in the scenario for the current ordering model. Based uponusing the EOQ model without instantaneous receipt (a.k.a., production run model):a. What is the optimal order quantity without instantaneous receipt?b. What is the maximum number of units in inventory without instantaneous receipt?c. What is the average number of units in inventory without instantaneous receipt?d. What is the average dollar value of inventory without instantaneous receipt?e. What is the total annual cost (i.e., Purchase Cost + Ordering Cost + Holding Cost)without instantaneous receipt?f. What is the optimal reorder point without instantaneous receipt?g. How many set-ups per year will be necessary without instantaneous receipt?4. The toilet manufacturer has proposed a quantity discount schedule for toilets as reflected inthe following table for consideration by the president of the wholesale distributor as a meansto potentially reduce his total annual costs.Discount Number123Quantity Ordered0 to 750751 to 1,5001,501 and overUnit Cost Discount0%7.5%15%The estimated annual demand for the toilets, estimated average demand per day, purchase costfrom the toilet manufacturer per unit, lead time for a new order, ordering cost per order andaverage holding cost per unit per year remain the same as stated in the scenario for the currentordering model. Based upon using the quantity discount model:a. What order quantity will allow the wholesale distributor to minimize total annualcosts (Purchase Cost + Ordering Cost + Holding Cost) by taking advantage of theproposed discount pricing?b. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) basedupon taking advantage of the proposed discount pricing?5. The president of the wholesale distributor is concerned about the possibility of stockoutscausing a loss of customer confidence and loyalty and is interested in maintaining safetystock in inventory to prevent potential stockouts. Based upon using the safety stock models:a. Assuming demand is normally distributed with a mean of 30 units and a standarddeviation of 4.5 units, and a constant lead time of 5 days, what is the reorder pointnecessary to provide a 97% level of service?b. Assuming demand is constant at 30 units per day, and lead time is normallydistributed with a mean of 5 days and a standard deviation of 1.5 days, what is thereorder point necessary to provide a 97% level of service?c. Assuming that demand is normally distributed with a mean of 30 units and a standarddeviation of 4.5 units, and lead time is normally with a mean of 5 days and a standarddeviation of 1.5 days, what is the reorder point necessary to provide a 97% level ofservice?2