Students in one class have received a group project for their course this semester. After hours of discussion, they reached to a point very close to the deadline, and they concluded that they should come up with a plan to accomplish the project. The plan requires a solid schedule, based on the nceds of the project. They realized they need $5,10,20,12,22,$ and $8$ students for hours of $0-4$ am$,4-8$ am$,8-12$ pm$,12-4$ pm$,4-8$ pm$,$ and $8-12$ pm$,$ respectively, Please formulate a linear programing model through which students can finish the project with minimum number of students However, the model should ensure faimess, so each student can begin working at midnight, $4$ am$,8$ am$,12$ pm$,4$ pm$,8$ pm$,$ and work for $8$ hours contimously on the project.