Classic Cars has created an improved automotive parts and tire offering to support its new and used BMW auto sales. The head of this new department Jenny Jackson wants to ensure that the reorder quantities for the various parts and tires have been correctly established. Jenny has decided to test one item to support her assumptions and will consider the Michelin tires, Defender size $185\backslash$times $14$ BSA. A perpetual inventory system has been used in the past and Jenny has created the following list of data:

Cost per tire $ $50$ each

Holding cost $25$ percent of tire cost per year

Demand $1,100$ per year

Ordering cost $ $32$ per order

Standard deviation of daily demand $7$ tires

Delivery lead time $8$ days

Because customers generally do not wait for tires but go elsewhere, Jenny has decided to use a service probability of $90$ percent. Jenny is assuming the demand occurs $365$ days per year.

a$.$ Determine the order quantity. $($Round your answer to the nearest whole number.$)$

Order quantity

$75$

tires

b$.$ Determine the reorder point. $($Use Excel's NORMSINV$()$ function to find the correct critical value for the given $\backslash$alpha $-$level. Do not round intermediate calculations. Round $"$z$"$ value to $2$ decimal places and final answer to the nearest whole number.$)$

Reorder point

tires