22 A company must complete three jobs. The amounts of processing time (in minutes) required are shown in Table 101. A job cannot be processed on machine j unless for all i< j the job has completed its processing on machine i.

Once a job begins its processing on machine j, the job cannot be preempted on machine j. The flow time for a job is the difference between its completion time and the time at which the job begins its first stage of processing.

Formulate an IP whose solution can be used to minimize the average flow time of the three jobs. (Hint: Two types of constraints will be needed: Constraint type 1 ensures that a job cannot begin to be processed on a machine until all earlier portions of the job are completed. You will need five constraints of this type. Constraint type 2 ensures that only one job will occupy a machine at any given time. For example, on machine 1, either job 1 is completed before job 2 begins, or job 2 is completed before job 1 begins.)