Carl's Custom Cans produces small containers which are purchased by candy and snack food producers. The production facility operates $320$ days per year and has annual demand of $13,200$ units for one of its custom cans. They can produce up to $190$ of these cans each day. It costs $$29\mathrm{.}23$ to set up one of their production lines to run this can. $($Carl pays $$14$ per hour for setup labor.$)$ The cost of each can is $$1\mathrm{.}70$ and annual holding costs are $$1\mathrm{.}90$ per can.

What is the optimal size of the production run for this can? $($Display your answer to the nearest whole number$).$

Given your answer to the previous question, how many production runs will be required each year in order to meet the annual demand? $($Round your answer UP to the next whole number.$)$

Suppose the customer for this custom can wants to purchase in quantities of $500$ units. What is the required setup cost to make this order quantity an optimal production run quantity for Carl's Custom Cans? $($Display your answer to two decimal places.$)$

Based on your answer to the previous question $($reduced setup cost$),$ how long $($in minutes$)$ should it take to set up this production line? $($Display your answer to the nearest whole number.$)$