11. Through its online accessory store, Gateway sells its own products, as well as products made byother companies. One of these products is the WB150 WolfByte laptop computer:Estimated annual demand:Cost:Lead time:Standard deviation of weeklydemand:Standard deviation of lead time:Holding cost per unit per year:Ordering cost:Desired service level:15,376 laptops (50 weeks peryear)$640 per laptop2 weeks16 laptops0.3 weeks40% of item cost$25 per order95% (z = 1.65)a. (*) What is the economic order quantity for the laptops? Calculate annual orderingcosts and holding costs (ignoring safety stock) for the EOQ.b. (**) What is the reorder point for the laptops? How much of the reorder pointconsists of safety stock?c. (**) Suppose Gateway decides to order 64 laptops at a time. What would its yearlyordering and holding costs (ignoring safety stock) for the monitor be?d. (**) Because computer technologies become obsolete so quickly, Gateway isthinking about raising holding costs from 40% of item cost to some higherpercentage. What will be the impact on the economic order quantity for laptops?Explain why.For parts e and f, use the following formula to consider the impact of safety stock(SS) on average inventory levels and annual holding costs:(+ SS) H e. (***) What is the annual cost of holding inventory, including the safety stock? Howmuch of this cost is due to the safety stock?f. (***) Suppose Gateway is able to cut the lead time to a constant 1 week. Whatwould the new safety stock level be? How much would this reduce annual holdingcosts?

EOQ is a statistical and mathematical concept used in production and operations management. It reveals how much quantity of units an organization should produce so that demand can be met and at the same time inventory-related costs can be minimized. This concept was introduced by F.W. Harris, an engineer in 1913. This concept tries to minimize the cost of ordering, storing, and using the inventory while it is in possession of the company. Today this concept is widely used by organizations and this model successfully solves the purpose it was originally designed for. This model help to order the perfect quantity of units so that stock levels in a business are never too low or in excess. Either of these conditions is not fruitful for any company under any given circumstances. This model helps to avoid that uncertain situation and lets the organization know how much to order without taking any financial risk in the future. Part a) - Computing EOQ Given, Annual Demand is 15,376 Unit Cost is $640 Holding Cost is 40% of unit cost 40% of $64040100 × $6400.40 × $640 = $256 The ordering Cost is $25 per order. EOQ = 2×Annual Demand × ordering costHolding cost = 2×15376×25256 =3003 =54.7 units. Annual ordering cost = Annual DemandEOQ × Ordering cost per unit= 1537654.7 ×25= $7027 Annual Holding Cost EOQ2 × Holding cost per unit54.72 × 256$7001 Part b) Calculating reorder point Reorder point = Average daily Usage × Average Lead Time Average Daily Usage = Annual DemandOperating days = 54.750 (weeks) = 1.09 Average Lead Time = 50 weeks2 weeks = 25 Reorder Point = 1.09 × 25 = 27.25 Reorder Point inclusive of Safety Stock Safety Stock = Z × ∑LT × D where Z is the desired service level, ∑LT is the standard deviation in lead time, and D is the average demand. Average Demand = 1537650 = 307.5 Safety Stock = 1.65 × 0.3 × 307.5 = 152.2Part c) If the company orders 64 units at a time, so given EOQ is 64. Revised Annual Ordering Cost = Annual DemandEOQ × Ordering cost per unit= 1537664 ×25= $6006 Revised Annual Holding Cost EOQ2 × Holding cost per unit642 × 256$8192 Part d) If the company attempts to increase the percentage of holding cost from 40 to a higher one, then as the percentage will increase, EOQ will start to decline. For example, let's say we change the percentage from 40 to 60%. Holding Cost = 0.60 ×640 = $384 Now when we calculate EOQ, the EOQ will be EOQ = 2×Annual Demand × ordering costHolding cost = 2×15376×25384 =2002 =44.7 units. Part e) Annual Inventory holding Cost with safety stock Q2 + SS H54.72 + 152.2 256179.55 × 256$45,964 Part f) New Safety Stock = 1 ×(16)2 +(307.5)2 ×(0.3)2 256 + 8510 8766 = 93.62 Q2 + SS H54.72 + 93.62 256120.97 × 256$30,968 Annual Holding Cost would be reduced to = $45964 - $30,968 = $14,996.