$17.$ Comparing EOQ with and without Backorders. A manager of an inventory system believes that inventory models are important decision$-$making aids. The manager has experience with the EOQ policy, but has never considered a backorder model because of the assumption that backorders were $$bad$$ and should be avoided. However, with upper management$$s continued pressure for cost reduction, you have been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. Consider a specific product with D $5800$ units per year, Co $5$ $$150,$ Ch $5$ $$3,$ and Cb $5$ $$20.$ Assume $250$ working days per year. LO $1,3$ a$.$ What is the difference in total annual cost between the EOQ model and the planned shortage or backorder model? b$.$ Suppose the manager requires that no more than $25\%$ of the units can be backordered and that no customer will have to wait more than $15$ days for an order. Should the backorder inventory policy be adopted? $18.$ Reorder Point for EOQ with and without Backorders. Assume the lead time for new orders is $20$ days for the inventory system discussed in Problem $17.$ LO $1,3$ a$.$ Determine the reorder point for the EOQ model without backordering. b$.$ Determine the reorder point for the EOQ model with backordering.