$22.$ Consider a single machine scheduling problem with $5$ jobs $(/1$ to J$5).$ The

minimum mean flow time for this problem is $25$ days. Let the job sequence

corresponding to this minimum mean flow time be denoted by S$.$

For simplicity, let S $=$ U$1,$J$2,$J$3,$J$4,$J$5\}.$ When the jobs are arranged in this

sequence, the respective job processing times follow an arithmetic

progression.

If the difference between the processing times of the last job $(/5)$ and the first

job $(/1)$ in this sequence is $16$ days, find the processing times of all the five

jobs.

$[4$ marks$]$