Problem:

$$ The current partially automated production line has $3$ mechanized and $3$

manual workstations that have an ideal cycle time of $1$ min $($includes a

transfer time of $6$ sec$).$ See table for data on each station.

$$ Your company wants to replace manual station #$5$ with automated one.

The new station would cost$$0\mathrm{.}25/$min with a probability $0\mathrm{.}02,$ but the

process time would only be $30$ sec which would reduce the overall cycle

time of the line from $1\mathrm{.}0$ min to $36$ sec$.$ The amount of time per

breakdown would not change with the automation and would stay at $3\mathrm{.}5$

min.

$$ The other costs of the system are as follows:

$$ Cost of the transfer mechanism $()=$ $$0\mathrm{.}10/$min

$$ Cost to run each automated station $()=$ $$0\mathrm{.}12/$min

$$ Labor cost to operate each manual station $()=$ $$0\mathrm{.}17/$min

$$ Find: For the current line and the proposed line:

$($a$)$ production rate, $($b$)$ proportion uptime, and $($c$)$ cost per unit.