Sam$$s Cat Hotel operates $52$ weeks per year, $6$ days per week. It purchases kitty litter for $$11\mathrm{.}70$ per bag.

The following information is available about these bags.

Average weekly demand $=90$ bags

Standard deviation of weekly demand $=15$ bags

Fixed order cost $=$ $$54/$order

Annual holding cost rate $=27\%$

Desired cycle$-$service level $=80\%$

Lead time $=3$ weeks $($or $18$ working days$)$

Suppose the owner manages the inventory with the continuous review policy: $($R$,$ Q$).$

a$)$ What is the economic order quantity based on the average demand of the year?

b$)$ What is the normal factor associated with a service level of $80\%?($look up the $$z$$ value in the

normal table$)$

c$)$ What should the reorder point be if the target cycle$-$service level is $80\%?$

d$)$ What is the total cost of the inventory policy, defined as the sum of fixed ordering and inventory

holding costs of a year? $($Calculate C$($Q$)$ for the continuous review policy$).$