A final assembly plant for a certain automobile

model is to have a capacity of $240,000$ units annually.

The plant will operate $50$ wk$/$yr$,2$ shifts$/$day$,5$ days$/$

wk$,$ and $8\mathrm{.}0$ hr$/$shift$.$ It will be divided into three

departments: $(1)$ body shop, $(2)$ paint shop, $(3)$ trimchassis$-$

final department. The body shop welds the

car bodies using robots, and the paint shop coats the

bodies. Both of these departments are highly automated.

Trim$-$chassis$-$final has no automation. There

are $15\mathrm{.}5$ hr of direct labor content on each car in this

department, where cars are moved by a continuous

conveyor. Determine $($a$)$ hourly production rate of

the plant, $($b$)$ number of workers and workstations

required in trim$-$chassis$-$final if no automated stations

are used, the average manning level is $2\mathrm{.}5,$

balancing efficiency $93\%,$ proportion uptime $$

$95\%,$ and a repositioning time of $0\mathrm{.}15$ min is allowed

for each worker.