The Enormous State University History Department offers three courses, Ancient,

Question

The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern History, and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 44 sections total, there are 5,100 students who would like to take a course, and there are 60 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of 2 professors, while Ancient and Medieval History need only 1 professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed to, accommodate all of the students, and give one teaching assignment to each professor?

Explanation / Answer

Lets say,

Ancient History is alotted= a sections

Medieval History is alotted= b sections

Modern History is alotted= c sections

Section contraint,

a+b+c= 44 .................... (i)

Professor constraint,

a+b+2c=60.....................(ii)

student constraint,

100a+50b+200c=5100

or, 2a+b+4c=102..............(iii)

from (i) and (ii),

c=16...............(iv)

a+b=28..............(v)

solving, (iii),(iv) and (v),

a=10, b=18, c=16

Answer,

Ancient History= 10 sections

Medieval History=18 sections and

Modern History=16 sections

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