Question 1. Instructors at the local community center are planning the summer schedule of music classes. They want to create a weekly schedule. There should be at most one class time each night, although multiple classes can be held at the same time. Appa teaches Harmonica, Iroh teaches Singing. Jet teaches Guitar, Suki teaches Bass, and Mai teaches Piano. Iroh wants to take the Bass class and the Harmonica class, Appa wants to take the Singing class, Jet wants to take the Harmonica class, and Mai wants to take the Guitar class. Everyone wants to take Piano. 1)a) Draw a graph with each class as a vertex, and draw an edge between any two classes that a single person wants to attend (either as an instructor or as a student). For example, Appa teaches Har- monica and wants to take Singing, so you should draw an edge between the Harmonica and Singing classes. 1)b) Find a proper coloring of this graph, using as few colors as possible. You should redraw the graph and color it with the 'colors' Mon, Tue, Wed, Thur, Fri, Sat, Sun. 21)c) Use your coloring to create a weekly schedule wherein everyone gets to attend all of the classes they are interested in, while using as few days as possible.
Question 1. Instructors at the local community center are planning the summer schedule of music classes. They want to create a weekly schedule. There should be at most one class time each night, although multiple classes can be held at the same time. Appa teaches Harmonica, Iroh teaches Singing. Jet teaches Guitar, Suki teaches Bass, and Mai teaches Piano. Iroh wants to take the Bass class and the Harmonica class, Appa wants to take the Singing class, Jet wants to take the Harmonica class, and Mai wants to take the Guitar class. Everyone wants to take Piano. 1)a) Draw a graph with each class as a vertex, and draw an edge between any two classes that a single person wants to attend (either as an instructor or as a student). For example, Appa teaches Har- monica and wants to take Singing, so you should draw an edge between the Harmonica and Singing classes. 1)b) Find a proper coloring of this graph, using as few colors as possible. You should redraw the graph and color it with the 'colors' Mon, Tue, Wed, Thur, Fri, Sat, Sun. 21)c) Use your coloring to create a weekly schedule wherein everyone gets to attend all of the classes they are interested in, while using as few days as possible.
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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Transcribed Image Text:Question 1. Instructors at the local community center are planning the summer schedule of music
classes. They want to create a weekly schedule. There should be at most one class time each night,
although multiple classes can be held at the same time. Appa teaches Harmonica, Iroh teaches Singing,
Jet teaches Guitar, Suki teaches Bass, and Mai teaches Piano. Iroh wants to take the Bass class and the
Harmonica class, Appa wants to take the Singing class, Jet wants to take the Harmonica class, and Mai
wants to take the Guitar class. Everyone wants to take Piano.
Q1)a) Draw a graph with each class as a vertex, and draw an edge between any two classes that a single
person wants to attend (either as an instructor or as a student). For example, Appa teaches Har-
monica and wants to take Singing, so you should draw an edge between the Harmonica and Singing
classes.
Q1)b) Find a proper coloring of this graph, using as few colors as possible. You should redraw the graph
and color it with the colors' Mon, Tue, Wed, Thur, Fri, Sat, Sun.
Q1) c) Use your coloring to create a weekly schedule wherein everyone gets to attend all of the classes they
are interested in, while using as few days as possible.
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