The Enormous State University History Department presents three courses, Ancient, Medieval, and Modern History, and chairperson is attempting to decide how many sections of each to present this semester. Department is permitted to present 46 sections total, there are 5,300 students who would like to take the course, and there are 62 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History have 50 students each, and sections of Modern History hold 200 students. Modern History sections are educated by the team of 2 professors, while Ancient present all sections that they are permitted to, accommodate all of students, and provide one teaching assignment to every professor?