The normal time for a work cycle in a worker$-$machine system is $6\mathrm{.}27$min. For setting the standard time, the PFD allowance factor is $12\%,$ and the machine allowance factor is $25\%.$ The work cycle includes manual elements totaling a normal time of $5\mathrm{.}92$min, all but $0\mathrm{.}65$min of which are performed as internal elements. Determine

$($a$)$ The standard time for the cycle

Machine time per cycle in minutes $T_m=$

Internal normal time in minutes $T_{\text{n}\text{w}\text{i}}=5\mathrm{.}3$

Standard time in minutes $T_{std}=$

$($b$)$ The daily output at standard performance.

Daily units produced in pieces $Q_{std}=1\mathrm{.}6$