A sporting goods company has a distribution center that maintains inventory of fishing rods. The fishing rods have

the following demand, lead time, and cost characteristics:

Average demand $=130$ units per day, with a standard deviation of $12$ units

Average lead time $=12$ days with a standard deviation of $1$ day

$250$ days per year in the business year

Unit cost $=$$$28$

Desired service level $=97\mathrm{.}5\%$

Ordering cost $=$$$53$

Inventory carrying cost $=25\%$

a$.$ What is the standard deviation of demand during lead time?

b$.$ How many fishing rods should the distribution center carry to provide the desired service level?

c$.$ What is the EOQ?

d$.$ What is the average cycle stock?