$12$ A job shop has four jobs that must be processed on a single machine. The due date and processing time for each job are given in Table $19.$ Use dynamic programming to determine the order in which the jobs should be done so as to minimize the total lateness of the jobs. $($The lateness of a job is simply how long after the job's due date the job is completed; for example, if the jobs are processed in the given order, then job $3$ will be $2$ days late, job $4$ will be $4$ days late, and jobs $1$ and $2$ will not be late.$)$