A loader operating has a $2\mathrm{.}5$cy heaped capacity bucket and swings on a $1\mathrm{.}2-$min load cycle. The trucks have $11-$cy capacity and a $30-$min haul$+$ dump$+$return time. A $95\%$ fill factor applies to the loader. The project works $50-$min hours.

a$.$ Determine the job production when using $5$ buckets to load the trucks.

b$.$ Calculate the unit cost in $$/$cy using these hourly rates: loader with operator $=$ $$90/$hr$,$ Truck with operator $=$ $$55/$hour$.$ Only need to consider the operation using $5$ buckets to load the trucks.