An important bookstore in Eastern Province sells smartphones that cost $3,000$ SAR per unit. The annual holding cost rate is $40\%$ per unit, the annual demand is $500$ units, and the ordering cost is $250$ SAR per order. Each order lasts $4$ days to be placed at the bookstore. The demand is variable with standard deviation of $2\mathrm{.}4$ units. The desired service level is $95\%$ and the store is open $320$ days per year.

a$.$ What is the optimal order quantity?

b$.$ What is the safety stock?

c$.$ What is the reorder point?

d$.$ If the bookstore settles a safety stock of $10$ units, what is the lead time?

with Stadord

Deviation

$=3000$

$=2\mathrm{.}4$