Problem $4$: $20$ points total. $23$ Suppose an outlet store is selling a new indoor grill. Demand is pretty good at $200$ items per week. The items cost the outlet $$10$ apiece which sell for $$69\mathrm{.}95$ per item. $4$ Order costs are about $$200$ per order due to shipping costs. The outlet's holding cost is $$6\mathrm{.}50/$item$/$year$.56$ Calculate the EOQ: $278$ A full truckload is $4000$ grills. The supplier is willing to mark down the price by $$0\mathrm{.}75/$grill to make transportation easier. How many should the outlet purchase at a time? $910$ TAC $($EOQ$)111$ TAC$($BP$)11213$ The outlet's lowest cost order $2.1415$ Suppose the order lead time is $3$ weeks. Also suppose that the standard deviation of demand per week is $40$ items. $16$ Assume constant lead time, what is the reorder point if the outlet wants to maintain a $95\%($z $=1\mathrm{.}65)$ service level? $1718$ ROP $=2$ Transportation Firm A $1920$ Suppose a new service promises faster service, but is less reliable. The new order lead time is $2$ weeks but with a $0\mathrm{.}5$ week standard deviation of lead time. $21$ What is the new reorder point if the outlet wants to maintain a $95\%($z $=1\mathrm{.}65)$ service level? Assume the standard deviation of demand is still $40$ per week. $2223$ ROP $=2$ Transportation Firm B $2425$ Which transportation company, A or B$,$ allows the outlet to have the lower total inventory costs? $2627$ Transportation Company $22829$ What is the expected fill rate for the grills if we order the EOQ amount per order, should the firm use Transportation Firm A$?3031$ Fill Rate $=23233$ What is the expected fill rate for the grill using Transportation Firm A if the standard deviation of demand doubled? $3435$ Fill Rate $=23637$ What would the increase in total cost be if the outlet went from the EOQ to weekly deliveries? $3839$ Increased Cost $=24041$ Ignoring price breaks, what would the order cost need to be such that weekly deliveries would be optimal? $4243$ Order Cost $=244$