Q$3.$ Derive expression for economic order quantity. A regional distributor purchases electric

appliances $($Mixers$)$ from various suppliers and then sells them on demand to retailers in the

region. The distributor operates $5$ days per week, $52$ weeks per year. Only when it is open,

business orders can be received. Management wants to reevaluate its current inventory policy

for following details.

Average daily demand $=100$ mixers

Standard deviation of daily demand $=30$

Lead time $=3$ days, Holding cost$=$$$9\mathrm{.}40/$unit$/$year$,$ Ordering cost$=$ $$35/$order

Cycle service level $=92\%(z=1\mathrm{.}41)$

Determine

a$-$ What order quantity Q and reorder point R should be used

b$-$ What is the total annual cost of the system?

c$-$ If on hand inventory is $40$ units, one open order for $440$ mixers is pending and no

backorders exist, should a new order be placed.