Spr $2024$ "During a particular $40-$hour week of an automated production operation, $381$ acceptable $($non$-$defective$)$ parts and $17$ defective parts were produced. The operation cycle consists of a processing time of $5\mathrm{.}23$ min, and a part handling time of $0\mathrm{.}58$ min. Every $50$ parts, a tool change is performed, and this takes $4\mathrm{.}2$ min. The machine experienced several breakdowns during the week. Determine the cycle time of the unit operation Tc in minutes.