$2\mathrm{.}4.$ Develop a table of the factory status at the beginning of each one$-$hour time interval for the following serial system under the condition that the system maintains a total work$-$in$-$process of $5$ jobs. Develop this table for the system status for $15$ hours of operation. The workstation processing times $($in hours$)$ are listed in the squares representing the workstations. The initial $($time $0)$ starting work$-$in$-$process distribution is $(5,0,0).$ That is$,5$ jobs in the first workstation and none elsewhere and assume that the first job begins processing at time $0.$ Compute the cycle times $($time in the system$)$ for the first $4$ completed jobs assuming that all $5$ initial jobs entered the system at siman

$2\mathrm{.}5.$ Reconsider Problem $2\mathrm{.}4$ starting with the initial conditions: work$-$in$-$process is $(2,3,0).$ Assume further that the first job in line at workstations one and two have already completed one hour of processing. Compute the cycle times for all jobs that are completed during the $15$ hours of operation, assuming that all $5$ initial jobs entered the system at time $0.$ Explain why the cycle times for the first $4$ completed jobs are not valid as the long$-$run average.