Cat Lovers Inc. $($CLI$)$ is the distributor of a very popular blend of cat food that sells for $$1\mathrm{.}34$ per can. CLI experiences a demand of $450$ cans per week on average. They order the cans of cat food from the Nutritious & Delicious Co$.($N&D$).$ N&D sells cans to CLI at $$0\mathrm{.}50$ per can and charges a flat fee of $$6$ per order for shipping and handling.

CLI uses the economic order quantity as their fixed order size. Assume that the opportunity cost of capital and all other inventory cost is $20$ percent annually and that there are $50$ weeks in a year.

$1.$ How many cans of cat food should CLI order at a time?

$2.$ What is CLI$$s total cost of ordering and holding for one year?

$3.$ Suppose the lead time to receive an order from N&D is $3$ weeks. Suppose the standard deviation of weekly demand is $100$ cans. What Reorder Point should CLI use to ensure a $98\%$ cycle service level? What would be the resulting safety stock?

$4.$ Consider the order quantity determined in part $1$ and the safety stock determined in part $3.$ What are CLI$$s inventory turns?