A beer distributor finds that it sells, on average, $100$ cases a week of Xinjiang Black Beer. For this problem assume that demand occurs at a constant rate over a $50-$week year. Beer is purchased at a price of $$8$ per case. The inventory$-$related holding cost rate is $25\%.$ Each order placed with the supplier costs the distributor $$10.$ Questions $($For each question select the choice CLOSEST to your answer$)$

$1.$ What order quantity $($Q$)$ minimizes the distributor$$s total inventory$-$related costs?

a$.5000$ cases

b$.100$ cases

c$.224$ cases

d$.448$ cases

$2.$ What is the expected number of orders that the distributor will place in a year?

a$.22\mathrm{.}4$ orders

b$.5000$ orders

c$.100$ orders

d$.$ Cannot be determined from the information given

$3.$ What is the average inventory level that the distributor can expect?

a$.224$ cases

b$.112$ cases

c$.100$ cases

d$.$ Cannot be determined from the information given

$4.$ What is the inventory$-$related annual total cost?

a$.$ $$447$

b$.$ $$224$

c$.$ $$7\mathrm{.}60$

d$.$ Cannot be determined from the information given