Question $5(8$ marks$)$

A manufacturing company needs to schedule the following seven jobs on a single machine. Each job requires a specific processing time, and the changeover costs between jobs depend on the job sequence. The processing times $($in hours$)$ and changeover costs $($in dollars$)$ between jobs are given in the table below.

Changeover Cost Matrix $($in $\backslash$$$)$:

a$)$ Determine the optimal job sequence to minimize the total changeover cost.

b$)$ Calculate the total changeover cost for the optimal sequence.

c$)$ Calculate the total time to complete all jobs. This includes:

$-$ The total processing time of all jobs.

$-$ The total changeover cost for the optimal job sequence.