Please show all steps and fully explain. This is an operational research problem.

In a scheduling problem, the vocabulary of manufacturing has been used because many of early developments in the scheduling field were motivated by problems in the manufacturing area. Thus, resources are usually called machines and tasks are called jobs. Now, consider the following manufacturing scheduling situation. A manufacturer must schedule jobs to to be processed on a single machine. It is currently the beginning of the day (0:00) and the information about 5 jobs that need to be processed is given in the following table. Consider 5 jobs having the processing times pj, the due dates dj (in mins) and the weights wj of the jobs j=1, 5, given in the table: 1 3 4 5 2 11 26 19 16 23 Jobs pj dj wj 30 45 15 60 40 180 12 45 75 252 Because all the jobs need to be processed, it is reasonable to assume that all jobs are already finished preparations to be processed and thus, they don't need ready times. Let's also assume that a job can start to be processed as soon as the previous job finishes processing and, as a consequence, there are no gaps between processes. Hint: this is a Job Shop Scheduling problem (n jobs, 1 machine) The goal is to minimize the weighted sum of completion times, develop the best schedule for these jobs