Chapter $9$:$2.$ Prince Electronics, a manufacturer of consumer electronic goods, has five distribution centers in different regions of the country. For one of its products, a high$-$speed modem priced at $$350$ per unit, the average weekly demand at each distribution center is $75$ units. Average shipment size to each distribution center is $400$ units, and average lead time for delivery is $2$ weeks. Each distribution center carries $2$ weeks supply as safety stock but holds no anticipation inventory.a$.$ On average, how many dollars of pipeline inventory will be in transit to each distribution center?b$.$ How much total inventory $($cycle$,$ safety, and pipeline$)$ does Prince hold for all five distribution centers?$4.$ Ruby$-$Star Incorporated is considering two different vendors for one of its top$-$selling products, which has an average weekly demand of $50$ units and is valued at $$75$ per unit. Inbound shipments from vendor $1$ will average $350$ units with an average lead time $($including ordering delays and transit time$)$ of $2$ weeks. Inbound shipments from vendor $2$ will average $500$ units with an average lead time of $1$ week. Ruby$-$Star operates $52$ weeks per year; it carries a $2-$week supply of inventory as safety stock and no anticipation inventory.a$.$ What would be the average aggregate inventory value of this product if Ruby$-$Star used vendor $1$ exclusively?b$.$ What would be the average aggregate inventory value of this product if Ruby$-$Star used vendor $2$ exclusively?c$.$ How would your analysis change if average weekly demand increased to $100$ units per week?$7.$ Southern Markets, Inc. is considering the use of ABC analysis to focus on the most critical SKUs in its inventory. Currently, there are approximately $20,000$ different SKUs with a total dollar usage of $$10,000,000$ per year.a$.$ What would you expect to be the number of SKUs and the total annual dollar usage for A items, B items, and C items at Southern Markets, Inc.?b$.$ The following table provides a random sample of the unit values and annual demands of eight SKUs. Categorize these SKUs as A$,$ B$,$ and C items.