$2.$ Kroger$$s grocery store is doing an inventory analysis for a popular cereal which has a demand of $20,000$ units per year. The cost of each box of cereal is $ $3\mathrm{.}20,$ and the inventory carrying cost is $$0\mathrm{.}68$ per unit per year. The average ordering cost is $$22$ per order. It takes about $3$ days for an order to arrive. The store is open $365$ days per year.

a$.$ What is the EOQ?

b$.$ What is the average inventory?

c$.$ What is the optimal number of orders per year