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 72 sections total, up to 8,000 students would like to take a course, and there are 96 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 $4,000 per section, Medieval nets $8,000, and Modern History nets $12,000 per section. How many sections of each course should the department offer in order to generate the largest profit? Let x = number of sections of Ancient History, let y = number of sections of Medieval History, let z = number of sections of Modern History, and let p = profit (in dollars). Determine the objective and the constraints needed to solve the problem. Objective minimize or maximize p = Constraints ? ≤ 72 ? ≤ 8,000 ? ≤ 96

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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 72 sections total, up to 8,000 students would like to take a course, and there are 96 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 $4,000 per section, Medieval nets $8,000, and Modern History nets $12,000 per section. How many sections of each course should the department offer in order to generate the largest profit?

Let x = number of sections of Ancient History, let y = number of sections of Medieval History, let z = number of sections of Modern History, and let p = profit (in dollars). Determine the objective and the constraints needed to solve the problem.

Objective

minimize or maximize p =

Constraints