The parts produced in a certain batch has to be processed through an average of $6$ machines.

There are $20$ new batches of parts launched each week. Other data as follows.

i$)$ Average operation time $=0\mathrm{.}1$ Hr$.$

ii$)$ Average setup time $=5$ Hr$.$

iii$)$ Average non$-$ operation time $=10$ Hr$.$

iv$)$ Average Batch size$=25$ parts. There are $18$ work centers in the plant and the plant operators for an average of $70$ production Hr$/$week$.$

Determine i$)$ Manufacturing lead time ii$)$ Plant capacity iii$)$ Production rate iv$)$ Plant utilization.