PLEASE DO NOT USE AI $!!$

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 $(T{p}_{ij}),$ and machine

fractions for each family member $(f_{ij}).$ Assume the nonoperation times $(T_{no})$ 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.