Teacher Scheduling Every semester the chairman of the CSSE department must assign faculty to teach the classes for the next quarter using the following information: • The list of courses and the number of sections that must be taught, along with their scheduled time slots. A course along with a time slot defines a possible section. Multiple sections of a course can be in the same time slot. E. g. 349-01 and 349-03 could both be MWF 10:00 a. m. or they might be in different time slots The list of faculty members along with each faculty member's time slot availability. That is, a faculty member may only be available for a certain subset of all the time slots. E. g. Mary may only be able to teach courses on MWF in the morning. Bill is only able to teach on TTH afternoons. • For each faculty member there is a list of courses that the faculty member is qualified to teach. In order for the schedule to be feasible there must find an assignment of faculty to sections subject to the following requirements: • Each faculty member is assigned to teach exactly two sections when the faculty member is available. The two sections assigned to a faculty member must be in different time slots • Each faculty member is assigned to teach only courses they are qualified to teach. Design a network flow model that will allow the department chairman to find a feasible schedule to this problem, or identify that no feasible schedule exists. Be sure to describe: • What each node, edges, and edge capacities represent in the network, • How to determine the assignment of faculty to sections that a given flow in your graph would represent. • How to know whether all the sections are covered - have a faculty member assigned to teach them.