Computer the capacity $($bottleneck rate$)$ in parts per hour of the following:

$(1)$ A balanced line with single$-$machine stations, all with average processing times of $15$

minutes.

$(2)$ A four$-$station line with single$-$machine stations, where the average processing times are $15,$

$20,10,12$ minutes, respectively for stations $1,2,3$ and $4.$

$(3)$ A four$-$station line with multimachine stations, where the number of $($parallel$)$ machines at

stations $1,2,3,4$ is $2,6,10,3,$ respectively. The average processing times at stations are $10,$

$24,40,18$ minutes, respectively.

$(4)$ A three$-$station with ample equipment $($i$.$e$.,$ such that operators are never prevented from

processing a job by a lack of equipment$)$ staffed by $6$ operators who are identical with

regard to average processing time and require $10,15$ and $5$ minutes, respectively on stations

$1,2$ and $3.(5)$ The same line as in the above case except that station $2$ consists of only $2$ parallel machines.

All other stations still have ample capacity.

until completion of the job? $($use memoryless property$)$

$($b$)$ A part is currently been processed on that machine for $30$ mins. What is the expected time

until completion of the job?