You manage the shipping of a few important motors from your supplier to your company's factory.

Demand for the motors is normally distributed with an average of $120000$ motors per year and an annual standard deviation of $9600.$ Your company currently purchases motors each year from the supplier at a price of $$127$ per unit.

The lead time for the delivery is $4$ days on average, with a standard deviation of $3\mathrm{.}5$ days. You use Carrier ABC, which charges $$6$ per motor, with a minimum shipment of $2000$ motors $($i$.$e$.,$ Q$=2000$ motors.$)$ Your company takes ownership of the shipment at the supplier$$s dock and will have to incur any holding costs from that point on$.$ Your company's holding charge is $14\%,$ a cycle service level of $95\%($given CSL$=95\%,$ use a k$=1\mathrm{.}64)$ and uses a $365$ days per year for planning purposes. Your company includes the cost of transportation in the cost of the motors when calculating inventory costs.