Using the fixed time period inventory model, and given an average daily demand of $75$ units, $10$ days between inventory reviews, $2$ days for lead time, $47$ units of inventory on hand, a service probability of $95\%($which corresponds to a Z factor of $1\mathrm{.}64)$ and a standard deviation of demand of $8$ units, calculate the order quantity. $(6$ points$)$

$q\frac{?}{b}=ar(d)(T+L)+z{}_{T+L}-I$

$q=$ Quantity to be ordered

$T=$ The number of days between reviews

$L=$ Lead time in days $($time between placing an order and receiving it$)$

$\frac{?}{\text{b}\text{a}\text{r}}(d)=$ Forecast average daily demand

$z=$ Number of standard deviations for a specified service probability

${}_{T+L}=$ Standard deviation of demand over the review and lead time

$I=$ Current inventory level $($includes items on$-$order$)$

Do this first

${}_{T+L}=\sqrt[\phantom{2}]{(T+L){}_d^2}$:

$q\frac{?}{b}=ar(d)(T+L)+z{}_{T+L}-$I