$4-$ 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 needs 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 fairness, so each student can begin working at midnight, $4am,8am,12pm,4pm,$

$8pm,$ and work for $8$ hours continuously on the project.