A printing company buys its paper supplies in rolls of $1,500$ pounds. The cost per roll is $$800,$ and the annual requirement is $2,500$ rolls. Each order costs $$50$ to process and the annual holding cost per roll is $15\%$ of a roll cost.

How many rolls should the company order at a time to minimize its total cycle inventory costs? $($EOQ lot size$)$ If the printing company in the previous question uses EOQ as its ordering lot size, what is the time between orders in days? Assume there are $250$ working days in a year. What is the total annual cycle$-$inventory cost for the company$$s current policy? $($using EOQ as ordering lot size$)$