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The Enormous State University History Department Offers Three Courses, Ancient

question 22

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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 ?

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Definitions:

Lower Mantle

The deeper section of the Earth’s mantle extending from 670 kilometers below the surface to the outer core, characterized by high pressure and temperature.

Continental Ice Sheets

Massive layers of ice covering large areas of continental land, primarily in polar regions, formed from accumulated snowfall.

Earth

The third planet from the Sun, characterized by its vast oceans, atmosphere, and life, supported by its unique position and geologic processes.

Sun

The star at the center of our solar system, which provides light and heat to Earth.

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