$(12$ points$)$ A store has collected the following information on one of its products:

Demand $=40$ units$/$day

Standard deviation of daily demand $=5$ units

Ordering costs $=$$$\frac{30}{?}$ order

Holding costs $=$ $$4/$unit$/$year

Customer service level for $95\%=1\mathrm{.}65)$

Lead$-$time $=10$ days

One year $=250$ operating days

a$.(7$ points$)$ If a firm uses the continuous review system to control the inventory, what would be the order quantity and reorder point?

b$.(5$ points$)$ The firm decided to change to the periodic review system to control the item's inventory. The review period is $10$ days. For the most recent review, an inventory clerk checked the inventory of this item and found $200$ units. There were no scheduled receipts or backorders at the time. How many units should be ordered?