A group$-$technology cell has three machines and is used to process a family of four similar parts. The table below lists production quantities $($Qj$),$ production times $($Tpij$),$ and machine fractions for each family member $($fij$).$ Assume the nonoperation times $($Tno$)$ are all the same at $30$ 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.