A sausage factory can produce European wieners at a rate of $580$ kg per day. It supplies wieners to local stores and restaurants at a steady rate of $110$ kg per day. The cost to prepare the equipment for producing European wieners is $$16.$ Annual holding cost is $$3$ per kg of wieners. The factory operates $280$ days a year. $($Round the final answers to the nearest whole number.$)$

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