A sausage factory can produce European wleners at a rate of $530kg$ per day. It supplies weners to local stores and restaurants at a steady rate of $110kg$ per day. The cost to prepare the equlpment for producing European wieners is $$11.$ Annual holding cost is $$4$ per $kg$ of wieners. The factory operates $320$ days a year. $($Round the final answers to the nearest whole number.$)$

a$.$ Calculate the optimal production run quantity. $($Do not round Intermedlate calculations.$)$

Optimal production run quantity

$kg$

b$.$ Calculate the number of production runs per year.

No$.$ of production runs per year runs $/$ year

c$.$ Calculate the length $($In days$)$ of a production run.

Length of a production run day$(s)$