XYZ factory operates $52$ weeks per year. It uses a part with code RW$1.$ Weekly demand for RW $1$ follows a normal distribution with a mean $90$ units and standard deviation of $15$ units. The cost of each unit of RW$1$ is $$11\mathrm{.}70.$ Holding costs are based on a $27\%$ interest rate. Lead time is given as $3$ weeks $($constant$).$ Ordering cost is $$54$ per order.

a$)$ What is the economic order quantity?

b$)$ If the desired service level $($Type I$)$ is $80\%,$ what is the safety stock?

c$)$ Determine the Reorder Point for the same service level as part b$.$