$(20$ points$)$ A certain part $is$ routed through six machines $in$ a batch production plant. The

setup and operation times for each machine are given $in$ the following table.

The batch size $is100$ and the average nonoperation time per machine $is12hr.$

$(a)$ Determine the manufacturing lead time

$(b)$ Determine the production rate for operation $3.$

$(30$ points$)$ The average part produced $in$ a certain batch manufacturing plant must $be$

processed through $an$ average $of$ six machines. There are $20$ new batches $of$ parts launched

each week. Other pertinent data are $as$ follows:

Average operation time $=6$min

Average setup time $=5$ hours

Average batch size $=25$ parts

Average nonoperation time per batch $=10$ hours

There are $18$ machines $in$ the plant. The plant operates $an$ average $of70$ production hours per

week. Scrap rate $is$ negligible.

$(a)$ Determine the manufacturing lead time for $an$ average part

$(b)$ Determine the plant capacity.

$(c)$ Determine the plant utilization

$(50$ points$)An$ average $of20$ new orders are started through a certain factory each month.

$On$ average, $an$ order consists $of50$ parts $tobe$ processed through $10$ machines $in$ the factory.

The operation time per machine for each part $=15$min. The nonoperation time per order $at$

each machine averages $8$ hours, and the required setup time per order $=4$ hours. There are $25$

machines $in$ the factory, $80\%20\%$ are $in$

repair $or$ maintenance