A group$-$technology cell has three machines and is used to process a family of four similar parts. The table below lists production quantities $(Q_j),$ production times $(T_j),$ and machine fractions for each family member $(f_{ij}).$ Assume the nonoperation times $(T_{n0})$ are all the same ar $30$ min per machine. Determine $($a$)$ average hourly production rate for the cell, $($b$)$ utilization of each machine and average utilization of the cell, $($c$)$ manufacturing lead time, and $($d$)$ work$-$in$-$process.

$\backslash$table$[[,Q($Machine$),$Machine $2,$Machine $3],[$Part$,a_j,T_{p1}(min),f_{1i},T_{p2}(min),f_{2i},T_{p3}(min),f_{3j}$