$15$ Find an optimal sequence for processing four jobs through five machines in the order Machine $1-$ Machine $2-$ Machine $3-$ Machine $4-$ Machine $5.$ The processing time data is given below.

$\backslash$table$[[\backslash$table$[[$Machines $/],[$Jobs$]],$Machine $1,$Machine $2,$Machine $3,$Machine $4,$Machine $5],[$Job A$,6,4,1,2,8],[$Job B$,5,5,3,4,9],[$Job C$,4,3,4,5,7],[$Job D$,7,2,2,1,5]]$

Also find the minimum total elansed time and idle time of the machines.