A large electronics superstore sells a popular handheld computer. The store presently manages its inventory of this item with the following process: When the number of computers in stock drops to $25,$ it places an order for $35$ to the manufacturer. $(25$ is called the reorder point and $35$ is called the order size.$)$ The amount of time to receive an order varies a bit but can be approximated by a normal distribution with a mean of $5$ days and a standard deviation of $0\mathrm{.}3$ days. An examination of sales records $($at times when there are computers in stock$)$ shows that the time between purchases of a computer is $2$ hours on average $($with an exponential distribution$).$ The store is open $10$ hours per day, $7$ days per week. The store estimates that during the next $2$ months, this demand pattern should remain steady. Management wants to satisfy at least $90\%$ of the customer demand directly from the store$$s inventory. Subject to this, of course, management wants to minimize its costs. In this case, the costs are $$100$ every time an order is placed $($regardless of its size$)$ and $$\mathrm{.}50$ per day for every computer that is in inventory at the store. Management wants to determine whether it

should change its reorder point and order size. Management has decided to consider a number of different scenarios in looking for a solution to their inventory problem. These scenarios are summarized by the rows in the following table.

For each scenario in the previous table, run $30$ simulations and report

the overall mean service level and the estimated total cost.

$1.$ Does this new reorder point achieve the desired service level of $0\mathrm{.}9$ or $90\%?$ If so$,$ which scenario would you recommend?

$2.$ As the order size increases, what happens to the ordering and holding costs?