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, 4 am, 8 am, 12 pm, 4 pm, 8 pm, and work for 8 hours continuously on the project