Jacob manages a candy store in a high traffic shopping mall. He has collected the following information:

Weekly demand for small candy boxes $=100$ boxes

Cost to place one purchase order with the box supplier $=$ $$15\mathrm{.}80$

Cost to hold one box for one year in inventory $=$ $$3\mathrm{.}45$

Lead time $=3$ weeks

Weeks in a year $=52$ weeks

Answer the next four questions based on the given data.

a$.$ What is the economic order quantity $($EOQ$)?$

b$.$ What is the average inventory level $($i$.$e$.,$ cycle inventory$)?$

c$.$ What is the total annual order and inventory$-$holding cost?

d$.$ If a fixed$-$period system $($FPS$)$ is adopted, what is the replenishment level $($M$)$ without safety stock?