LuxeLife store resells luxury items, the demand for which is normally distributed. The inventory related information at the LuxeLife store is as follows:

Average Annual Demand $=400$ luxury items

Standard deviation of weekly demand $=2$ items

Item Cost $=$ $$4,000$ per item

Ordering cost $=$ $$2,500$ per order

Lead time $=10$ weeks

Annual inventory$-$holding cost estimate $=1\mathrm{.}25\%$ of the item cost

Required service level $=90\%$

LuxeLife works $50$ weeks a year.

Note: The approximate z values are: for $0\mathrm{.}91\mathrm{.}28,$ for $0\mathrm{.}921\mathrm{.}405,$ for $0\mathrm{.}951\mathrm{.}645,$ for $0\mathrm{.}982\mathrm{.}05.$

Suppose the store management practices the fixed$-$QUANTITY ordering system with the use of the economic order quantity. Answer the following questions:

$($i$)$ How many luxury items they order each time?

$($ii$)$ When do they place an order?

$($iii$)$ What is the safety stock?

Select one:

a$.$

$($i$)$ they order $200$ luxury items

$($ii$)$ an order is placed when the inventory in stock reaches about $80$ items

$($iii$)$ the safety stock is $8$ items

b$.$

$($i$)$ they order $288$ luxury items

$($ii$)$ an order is placed every $2$ weeks

$($iii$)$ the safety stock is $88$ items

c$.$

$($i$)$ they order $200$ luxury items

$($ii$)$ an order is placed every $4$ weeks

$($iii$)$ the safety stock is $128$ items

d$.$

$($i$)$ they order $280$ luxury items

$($ii$)$ an order is placed every $10$ weeks

$($iii$)$ the safety stock is $80$ items

e$.$

$($i$)$ they order $200$ luxury items

$($ii$)$ an order is placed when the inventory in stock reaches about $88$ items

$($iii$)$ the safety stock is $8$ items