A$)$ The time to load a starting work part into the production machine in a certain unit production operation $=0\mathrm{.}40$min, the actual processing time in the operation $=3\mathrm{.}10$min, and the time to unload the finished part $=0\mathrm{.}20$min. In addition, the tool must be changed every $5$ cycles and the tool change time $=1\mathrm{.}50$min. What is the cycle time for the unit operation?