Demand for a product is $1,000$ units a month. Lead time is Normally distributed

with a mean of $2$ months and a standard deviation of $0\mathrm{.}5$ months.

a$.(3$pts$)$ What reorder level and safety stock give a $98\%$ cycle service level?

b$.(3$pts$)$ What is the best reorder quantity if the reorder cost is $$2,500$ and the

holding cost is $$0\mathrm{.}5$ a unit a month?

c$.(3$pts$)$ Now, suppose that demand is also Normally distributed with a mean of

$1,000$ units a month and a standard deviation of $200$ units a month. What reorder

level gives a $98\%$ cycle service level? $(3$pts$)$ Justify the difference between reorder levels in $($a$)$ and $($c$).$

What is the total annual relevant cost associated with $($c$)?$