Question $2[30$ points$]$:

A sporting goods company has a distribution center which maintains inventory of fishing rods. The fishing rods have the following demand, lead time and cost characteristics:

Average demand $=100$ units per day, with a standard deviation of $12$ units

Average lead time $=12$ days with a standard deviation of $2$ days

$250$ days per year in the business year

unit cost $=$ $$25$

desired service level $=95\%$

Ordering cost $=$ $$50$

Inventory carrying cost $=20\%$

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

b$.$ What is the EOQ?

c$.$ What is the total acquisition cost $($please include the annual product cost in your calculations$)?$