The Enormous State University History Department Offers Three Courses, Ancient

Multiple Choice

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 50 sections total, up to 6,000 students would like to take a course, and there are 60 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 What is the largest profit possible Will there be any unused time slots, any students who did not get into classes, or any professors without anything to teach ?

A) the department should offer 40 sections of Ancient History, 10 sections of Medieval History, and no sections of Modern History, for a profit of $1,100,000, there will be 2,000 students without classes, but all sections and professors are used.
B) the department should offer no sections of Ancient History, 40 sections of Medieval History, and 10 sections of Modern History, for a profit of $1,100,000, there will be 2,000 students without classes, but all sections and professors are used.
C) the department should offer 10 sections of Ancient History, no sections of Medieval History, and 40 sections of Modern History, for a profit of $1,100,000, there will be 2,000 students without classes, but all sections and professors are used.
D) the department should offer 40 sections of Ancient History, no sections of Medieval History, and 10 sections of Modern History, for a profit of $1,100,000, there will be 2,000 students without classes, but all sections and professors are used.
E) the department should offer no sections of Ancient History, 10 sections of Medieval History, and 40 sections of Modern History, for a profit of $1,100,000, there will be 2,000 students without classes, but all sections and professors are used.