t is your responsibility, as the head of the automotive section of Nicholas Department Store, to

ensure the recorder quantity for the various items has been correctly established. You decide to

test one item and choose Michelin tires, XW size $185$x$14$ BSW$.$ You find the following

information according to historical data:

Cost per tire $$35$ each

Holding cost per unit $20\%$ of the tire cost per year

Demand $1000$ per year

Ordering cost $$20$ per order

The standard deviation of daily demand $3$ tires

Delivery lead time $4$ days

Because customers generally do not wait for tires but go somewhere else in case of a stock out,

you decide on a service probability of $98\%.$ Assume the demand occurs $365$ days a year $($your

store opens $365$ days a year$).$

$1.$ What is the optimal order quantity