Q$1$: Central University uses $$123,000$ of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $$45$ and thinks that the university can hold this type of inventory at an annual storage cost of $22\%$ of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying? $($Assume purchase price $=$ $$1)$ Q$2$: A Hospital stocks a kit that has a normally distributed demand during the reorder period is $400$ kits, and the standard deviation is $15$ kits. The hospital administration wants to follow a policy that results in stockouts only $10\%$ of the time$($i$)$ What is the appropriate value for Z for $10\%$ stockouts$($ii$)$ How much safety stock should the hospital maintain?$($iii$)$ What reorder point should be used? Q$3$: The average daily demand for laptops at Best Buy is $20,$ with a std$.$ deviation of $5$ units. The lead time is constant at $2$ days. Find the reorder point if management wants a $90\%$ service level $($i$.$e$.,$ risk stockouts only $10\%$ of the time$).$ How much is the safety stock?Q$4$: Amazon sells about $100$ digital cameras a day $($demand $=$ constant$).$ Lead time for camera delivery is normally distributed with a mean time of $5$ days and a standard deviation of $2$ days. A $98\%$ service level is set. Find ROPQ$5$: An electronic stores most popular item is six packs of $9$ volt batteries. About $140$ Packs are sold per day, following a normal distribution with a standard deviation of $9$ packs. Batteries are ordered from an out of state distributor. Lead time is normally distributed with an average of $4$ days and standard deviation of $1$ day. To maintain $95\%$ service level, what ROP is appropriate?