large electronics superstore sells a popular handheld computer. The store presently managesits inventory of this item with the following process: When the number of computers in stockdrops to $20,$ it places an order for $35$ to the manufacturer. $(20$ is called the

reorder point$$and $35$ is called the$$order size$.)$The amount of time to receive an order$$varies a bit, but can beapproximated by a normal distribution with a mean of $5$ days and a standard deviation of $\mathrm{.}3$ days.An examination of sales records $($at times when there are computers in stock$)$ shows that the time$$between purchases of a computer is $2$ hours on average $($with an exponential distribution$).$Thestore 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$$store$$sinventory$.$Subject to this,$$of course, management$$wants to minimize its costs.$$In this case,$$thecosts 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$$the stor aced $($regardless of its size$)$ and $$\mathrm{.}50$ per day for everycomputer that is in inventory at$$the store.$$Management wants to determine whether it shouldchange its reorder point and order size.$$

$50$

$$

$50$

$50$