The Enormous State University History Department Offers Three Courses, Ancient

The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern History, and the department chairperson is trying to decide how many sections of each to offer this semester. They may offer up to 40 sections total, up to 5,000 students would like to take a course, and there are 50 professors to teach them (no student will take more than one history course, and no professor will teach more than one section). Sections of Ancient History have 100 students each, sections of Medieval History have 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. Ancient History nets the university $10,000 per section, Medieval nets $ 20,000, and Modern History nets $30,000 per section. How many sections of each course should the department offer in order to generate the largest profit

The department should offer __________ section(s) of Ancient History, __________ section(s) of Medieval History, and __________ section(s) of Modern History.

What is the largest profit possible

The profit is $__________.

Will there be any unused time slots, any students who did not get into classes, or any professors without anything to teach

There will be __________ student(s) without classes, __________ professor(s) without anything to teach, and __________ unused time slots.